{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unit Root Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_This setup code is required to run in an IPython notebook_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.simplefilter('ignore')\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn\n",
    "\n",
    "seaborn.set_style('darkgrid')\n",
    "plt.rc(\"figure\", figsize=(16, 6))\n",
    "plt.rc(\"savefig\", dpi=90)\n",
    "plt.rc(\"font\",family=\"sans-serif\")\n",
    "plt.rc(\"font\",size=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most examples will make use of the Default premium, which is the difference between the yields of BAA and AAA rated corporate bonds. The data is downloaded from FRED using pandas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tVTtr7mHIdhwtFqyqW03Dr3ASOAEAAICNiJZarKhs2YoYlYplLdMbGpQv1QZO9/8pcAIAAAAbE4ETKypajqKRxn8q7pRaR4Vy9f4nfoWToUEAAADAxkRLLVZUsuxg/WY9hmHIkYLA+c6XXaC9m1KVCiclTgAAAGBDInBiRSXLUXy5Cqfctlk/cD5nz7gumByS5LbV2g2/EwAAAMB6RkstVlSy7Lr7b/r8L/mBMxGt/FkZhkGFEwAAANigCJxYUdGyq0JkLcNbq5nzhgYlQ/eNGEypBQAAADYqAidWVLScYEuUevzaZz6ocEaCr5mGIYueWgAAAGBDInBiRcXy8hVOs6bCGb5vxDSocAIAAAAbFIETKypa9vJDg7wSZ75kyZCqJtoaNS212aKlv7z10JI9OwEAAACsPwROrKhYthVbbg2n9/+5kq141AzWdEpSxDAUnhn05XuO6/N3HdMX7z6+RkcLAAAAoF8QOLGiomUrsWyF0w2Y+ZJVNTBIctttwxVOy0ufOSqcAAAAwLpH4MSKipZbuWzE3xYlV1q61tM0jSBkSgpac0sW6zoBAACwtizb0WOnF3t9GBsagRMrKpZtxSON9+H05cvWksAZMaTwzKCo93NKjK4FAADAGvv+k1P65c/drVPz+V4fyoZF4MSKipaz7NAgM9RSG94SRXLbba1Q4vQrm1Q4AQAAsNamM0VJ0myu1OMj2bgInFhRsbx8S20wpbbO9imR2im13trNQpk1nAAAAFhb/tyQLPNDeobAiRWtvC1KZR/OldZw+tuhzOfLa3CkAAAAQIUfOHNFlnP1CoETK1ppaJC/vDNbrBM4a7ZFyRYJnAAAAOiOrBc0qXD2DoETy7IdRyXLWXZokF/9XCiU6wROyQm11OaocAIAAKBLKhVOAmevEDixrGLZvSq0XEttIuZ+bbFQv8Jp1alwzuVZuA0AAIC1xRrO3iNwYln+NNnlWmoToTCarJlSGzEN2TYVTgAAAHRfUOEkcPYMgRPLKlhNVDhDIbN+hTMcON2fV7adqum1AAAAQKf53XVZWmp7hsCJZZX8wLlMhTMerazvTMbqreGsfB5uZyizFycAAADWEBXO3iNwYlmFZtZwhiqcyVh1S+2SCmfo6lLJZjw1AAAA1o7fXUeFs3cInFhWMDSoyTWcqTqBs94aTqmyPrSffP+Jc7rz6EyvDwMAAAAdkKXC2XMETiwraKldZluU8LrNVE1LbcRU1VrNXMnScMINpWWr/yqc7/r6w3rrPz7Q68MAAABAB/jddUyp7R0CJ5bVzNCgcPWzdkqtaRjyC5xly1bRcjSajEmSSnZ/VThLfRiAAQAA0L4s+3D2HIETyyqV3VBYO302bLkKp2lUKpyL3hN9IuUGzn4bGnR8Nt/rQwAAAECHWLYTzCPJligs9AqBE8vyK5yxZYcGhSqcsaX7cFpeJTNTdPfeHE/5Fc7+euIfnc31+hAAAADQIflyparJGs7eIXBiWU0NDaoKnNX3i0XMYDjQYsF9oo+lopL6b2jQ0Rk3cNZWaQEAADB4wm20TKntHc6ssaxiE2s4o2ZloFDtlNpYxAx+Rm2Fs9+GBp1dLEha/t8KAACAweB36o0kolQ4e6jpM+vPf/7zeuUrX6lrrrlG11xzjV73utfp1ltvXcNDQz/IexXO5DIVTsMIBc6aoUHxiBEM48l4Fc6gpbbPKpz+C5H/bwYAAMDg8meRjKWiyhYtOU5/nXtuFNFm77ht2za9613v0t69e2Xbtm666Sb99m//tr7yla/okksuWctjRA/5C61rW2UbqddSW7T8NZzVgbPcZ1Nq/Y2BC2Vblu0oYjbeCgYAAAD9ze+yG0vGdEx5Fcr2knkjWHtNB87rrruu6vN3vOMd+uIXv6h7772XwLlOFcu2MgW3DbZ2u5NGap/EsVCFc7HQ30OD8qFWi0LZVjrOCxIAAMCg8s9B/fkh2ZIlR0uXgGFttbVYzbIs3XLLLcpms7r66qs7fUzoEy/8Xz/QJ354RIbc4NiM2idwPDQ0yK9w9uvQoHBv/yd/eCSYrgsAAIDB43fZjXl7wH/6x0d17V/dpnOZYi8Pa8NpusIpSY899phe//rXq1AoKJ1O66Mf/agOHDiw4vcZhjQ+nm77INFbqXhEExNDTd136+ahqjWdw+m4Srat8fG0LMNQxDS0Y/OwJCmejPXV30UplC8/f9cxPe+iSf3sM7f37oA6IBIx++q/MbCR8PwDeoPnHnzxqawkaet4SpL05XtOSJKcWJS/kS5qKXDu27dPN910k+bn5/Xtb39b73nPe3TDDTfo4osvXvb7HEeanc2u6kDRO4mI2fTvb26uei9Lp2ypWLY1O5vVufm8huMRFbLuVaX5hXxf/V0s5EpVnxdypb46vnaMj6cH/t8ADCqef0Bv8NyDb3YuL0lKGrW3ZzUbZ1eCTtuyZaTu7S39l47H4zr//PN1+eWX6/d+7/d06aWX6h/+4R86cXzoM4XQpNZmBwbVE4uYsh13QFCmWNZQPKKo157bjy21Q6F1m0Os4QQAABhYwdAgb35I5fb+Ogdd71YV7W3bVrFID/R6tOAN+JGkxDJboqzE39OyZNnKFCwNJaKKhW7rJ7mSrYl05QWJNZwAAACDKxgalKxu6iyxBV5XNd1S+5GPfEQvfelLtX37dmUyGd18882644479IlPfGItjw89shgKnM1OqK0n5oXVYtlWplhWOhZR1NtupNRngS5fsrRzNKljs277Rb9N0QUAAEDzGlc4OcfrpqYD57lz5/Tud79bZ8+e1cjIiA4cOKC/+7u/04tf/OK1PD70SFXgbKKl9pY3PVf5OleLYqFw6W81Egtaavvnye44jnIlq6rC2W8tvwAAAGie3zo7nqwOnJzjdVfTgfNDH/rQWh4H+kyrFc6tI4m6t4dbaouWo/GIGbTU9lPLatFyZDvSRCocOPsnEAMAAKA1fuusvyWfjwpndzGeCXUtFCp7UkbM5vbgrCcWdb+3WLZVLNtKRM1K1bOPri75e3COhyqc5T4KxAAAAGiNHyyHEzVrOAmcXUXgRF3hCqfltB+8KhVORwXLVixiBgG2n57seS9wbkpT4QQAAFgP/OJG7QBMKpzdReBEXeHA6awicPrts0XLrXDGo6YMw1DUNPpqaFCu5L7wbE7H9ak3XCWpvyqwAAAAaI0fLKM13Xpsi9JdBE7UVV3hbP/nxEMDgoqWrYQXQGMRo68qiH5LbTIW0fkTKUn9N0UXAAAAzStZtuIRQ4Zh6HnnT+g/XL7dvZ1tUbqq6aFB2FjCazg7XeH0b++noUF+4EzFKkONyn0UiAEAANCaouUE53V//drLlSmWddMDp2ip7TIqnKjLX9MoSavJhZXA6ahoVQJn1DT6qmV1KlOUJI0lY6FtW/rn+AAAANAat8JZiTuJUCEE3UOFE3WFn4j2KhKn31KbL1myncrnbuDsnyf7T56e1VA8ogu2DMk7xL46PgAAALSmWLaDQoLk7rxgiDWc3UbgRF3hJ2InKpz+mtB4pNJS209rJO84MqufOm88WFQeNQ22RQEAABhg4e46STIMQ/GoyRrOLqOlFnWVLFvnjScVMQ39+vP2tP1z/ICZKbotuoloZWhQv6yRzBYtHZ/L67IdI8Ft7lAjAicAAMCgKoXWcPpiEYOW2i6jwom6CmVbE+m4vvrrz1nVz/HbGOpVOPulgjifL0mSxlOVPTjd4+PFCADQ2B9/+6B+6rxx/eylW3t9KADqKNas4ZTcc1GKCt1FhRN1lWpaENrl/4xFb+ptPw4Nms+7YXg0Wbn+0k/HBwDoP/mSpa8/cErv+9ajvT4UAA3426KExSImFc4uI3CirqLlLHmCtiNm1l/DGTXNvhnKs+Ad20gocMYi/XN8AID+c3g62+tDALCCYp2W2nif7QW/ERA4UVexvLQFoR1+S62/hjMeWsPZL0ODKhXOcEtt/xwfAKD/HJqqBM5caCsxAP2jdlsUya9wco7XTQRO1FWv570dfsDMFN1Ql4gsPzToibMZHZvNrfpxW7FQp6U2Zpp9M9QIANB/woHz2r+6TQWmXgJ9p3ZbFMlfw8nztZsInKirWLYV68AaTtMwFDUNLRRqK5xLhwY5jqM3fPYuvfpTd676cVsx5w0NGkmE1nAypRYAsIwTc/lg8rokzeZKPTwaAPWULGfJTJJYxOQCUZcROFFX0bKDauRqJaKmFrxQ568LrTeU5+iMW9nsZsx74MS8/upfn1LEkIbikeD2qGmoxJRaAEADhbKt8ydSev/PHZBEWy3Qj8q2Heyx7ktEWcPZbQRO1FW0lrYgtCsZiwTrJCtTape2M9x+ZDb42HG6Ezt//5sPS5Isx90M2BdjZDYAYBnFsq1E1AwuVuYJnEDfsWxHEbPelFrO8bqJwIm6SpZT1Sq0GsmoWQmckcZDg46EJv7N5codeeyVbB1J1L290RpTAAAkqVC2lIiaSsbcwJkr8Z4B9BvLkSIGazh7baAD5/G5XFVIQWc4jqNC2V4yRrpdyZgZtMkmoo2HBoXbkU4u5CVJD59a0HUf+6HOLhY6ciy1zhtP1b09ZppMqQUANFTw1oalgsBJhRPoN5btyKxX4WQNZ1cNdOD8D//7Tr3273+ip6ayXWvB3Aj8YT6dmFIrScloZW3kckOD8qEn/69+7h4tFsr6+gOnNJcv658ePduRY6llecdw+Y6RqtujEUNl2i0AAA3424elYu77GoET6D+24yxZwxlnDWfXDXTg9P2nf/iJvvf4uV4fxrpR9J6EtVO92hVuzfVDbL2hQbmSpV1jyeDzh04uaPe4+/mT5zIdOZZa+bKt/ZvT+tQbrqq6PRYxGRoEAGioaLlrOKlwAv3Lsp0lLbVR01hS9MDaGqjAeWw2pw/9y+P69qNn6nwt34MjWp/8NoN4x4YG1QucS/vn8yVLW4bj+tyvXCNJOjKTC0LpWgXOQtnSUDxaNTBIkmJ1AjEAAL6CV+FkDSfQv8oNWmo5x+uugQqc//ToGX3lvpP6n999ckkL7VAi0uC70Cp/clenW2ojhoLJt/WGBuXLtpLRiC7eMqR0LKKjM1lliu4V4+Nza3NBIV+yqwKxj6FBAIDlFMq2t4bTfQ9hSi3Qf2yHCmc/GKjAeXaxKMndXPngmeqKV7bIC32nBBXOTk2p9d6MhxOVSmIsYsiynaoLB7mSpWTMlGEY2jOR0tGZnLJFd1rtQr4crLfspLw31r5WNGJqsWjp5z/xY/3g0FTHHxcAMNj8bVH8i6q01AL9p962KFHTVJllU101UIHznBc4Jelfn6wOAYuF7myjsRH4azg7NqXWezMeSUaD2/yfHb7ClCvZwVqYPRMpHZnJBW/gjtzQ2Wn5klU11MgXNQ3N58s6u1jUX33/qY4/LgBgsBUst6U2YhpKRE1aaoE+5AbO6tuiEZZNddtABc4ziwU9e8+4huIR3fzw6aqvLRS4stgpwdCgDgVOv4I4kqgETn9iWPgJny9ZQeDcMpzQdKYYtNRK0my+1JHjCcuX67fUhqueqTjt2gCAirLtyLIr+1UnoyYVTqDPOI5Tdx/OmNdSyw4X3TNQgfNcpqgdown9wjO26YS3pu8vX32ZtgzHqXB2UKWltrNDg6oCpxdmw4ODwuspR5NR5cu25kNVzblc5wNnoWwrWaeldvtoZVpuuk4gBQBsTN9+9IwePDEvqXJxMhWLsIYT6DN+E92SllpvnshaLNVCfQNzJv1vT07p7GJRk8MJveFZu4LbL5oc0qZ0XAuFsm57alrnMsVlfgqa0ekKp9+y6lcvJffqkqRgcJDjON4aTvc+w144Pb1Q0KjXiju3Vi21saUVzN2h7VnqfR0AsPGULFv/7ZZH9Ztfvk9S5X0yFYvQUgv0GdurYNZbwymJwUFdNBCBs1i29c6bHpIkjSWj2j2e0m8+f4+2Dse1KR3TSCKiuVxZb//qg/qNL97b1mM8enpBv3zD3ZrOElg7PqXWqxDGQtus+B/7k2ALZVuOpJTffpt0Q97phYK2jyQkdb7C6ThOw6FBu8aTdb4DALCRHTyzWPW5P1wvGaOlFug3fgVzSUttZOmyLqytgQicj4Ze4A9sHZYkvekFe3Xzm56raMTUcCKqM4sFSe1vn5M4k+4AACAASURBVPHle07osTOLuuWh0yvfeZ3r+JTaqB84Kz+vdmhQ3ntMv5rot9+WbUc7vWpjpyucBf8x6/w7d4ZaamnXBoCNK1eygovR959ckFQ5YaWlFuhf/jlm7T6c/hwRJtV2z0AEzge8tRJf/S/P1rPOGw9u97fYGE5EdXqh0PbPL1l2UHb/t0PTqzjS9SEInB2qcPq/p/DPqx0a5L9Rp+qs95wciitiGh2vcBZqQm5Y+LZFBlIBwIb1q5+7W6/4+I8lSQ+ddM9HYl5LHi21QP9q2FIbzBGhwtktAxE4Hzm9oO0jCZ03kar79eFQOJHU8tSpX/jE7frWw2ckSfccm9N3D55t70DXiWxN+Fst/wkdDbXU1g4N8t+o/XWe4S1UhhJRjSWjmuvwlNr8MhVOSXrri/ZKosIJABvZ4elc8PGhqaykyvuk3wk0nIhogfcKoK80aqmtVDgJnN0yEIHzXKao7aOJhl8fSVRXqFppvbQdRzNe5exnDmzRtpGE/vmxjR04/XUoQ/HoCvdsjt+yEK5w1g4Nypfdx0xEq1tq3eOIaDwV03Smw4HT+3cmGgTrNz53j1539U4tFjmJAICNzrIdHZnOVt3mt9ROpOOaXYNJ6gDaFwTOmtO8YI4IgbNrBiJwzuXKGkvGGn699mtHZ3IN7rnUucXKkKBE1NSuseSGn3Tr733Zqf0n/fWaY6lo6LbqoUG5ZVpqU7GItgzHO/57qVQ4G/87hxJRZQpW0JYBANiYjs3mVLScqu6fhPf+NpGKKVO0gqUaAHrP75hdWuFcujUf1tZgBM58qSqs1BpPVQfOHz7V/DpMf8jQs/eM660v2qvJobimNnjgzBYtJaJm0HKwWv/h8u1664v26pd/6rzgttqhQbUtteHJsfs2p7VlOKGzi+2v062nsoaz8dNgOB6RIzF9EAA2oPASncfPZiRJz9wxGtwWDyqc7nnIDJPugb5RqXDSUttrfR84HcfRXK60bIUzHDh3jyf1Ly20xB6bdauh773uIm0ZTmjzUOcraYMmV7KU7uDek7GIqTc+d09ViKwMDXJDnx/y/TdtI3Q16qpdY9oy7F4I6GSl0W+pXa7C6a8PZnAQAKxP//TIGd3WYGBg+LX/5Lx7gXpvaJ5EEDi98xDaaoH+0WhoUG2XHdZe3wfOfNlW0XI0lmoucF57wWYdmck1XSY/PpeXaShYIzo5FFeuZCtb3LgBI1O0lO5QO20jtRPCjs/mFDGk7aNL979MRE1NDiVkOdJ0tnNv5vkmKpx+a+98hwcWAQD6w3//1qN6+9cerPu1qVDFcjbnruffNBQPbgtaar2LpZ18jwKwOmWGBvWNvgyc2aKlHxyakqRgK4yxZOOW2nC77bYRNzg2O1n01EJBk0PxoMVzs/dGstHaau85Nqdn/9m/6sRcXtkuBM7aoUHH5/LaPpqsauP90n9+lr75m8+RJG0ddn8v5zrYVhsMDVpmv9Hd424Avv6zd+sj332iY48NAOiux04v6vGziyvfMWQ6FDj9Semb05WL3PHQ0CCJCifQTxq11MbYFqXr+jJw/vmtT+odX3tIj59d1Jx3RbHZCqffettsC+TUYlGTw5UJuJNe4NxobbXfePCUJOnOozPKdriltp5gDadXiT4+l9euserq5gWTQ0HFc4sXOM8udu730szQoL2b0sHHX77nRMceGwDQPSXL1i9/7m5d/9m7W/q+mVDFci5XUsQ0NBpa4uNfpPZbameocAJ9w2+pNRuu4aSltlv6LnAu5Ms66o0dPzFX0Kx3RXG5oUHJUDga9rZIyTS5lcVUthiETKny5rHRAqdf5SuU7e5UOGtGUh+bzWvX+NJ2Wt82L3i2MoF4Jc0MDUrWBO9W1pA+cTajD3z7IBNuAaDHvnPwXPBxKx1MmdDymrl8WamYWfX+6J+4DiciipoGLbVAH2m4D2fN4Eqsvb4KnLcdmtZPf+yHuuf4vCTpxHw+1FLbuMIZ1uqQl6lMUZuHKj/bb8k9vdDZiaj9rjpwltd+Daf3Jv3n33tS09miZnMl7RpLNbz/5FBceyZS+snTsx07hmaGBtU6MZfXNx44pR8fXnkS8tu/9qBueuCUzmywvyUA6DeHpjLBx3ccnQk+Ds97qHdxMPz1uVxJyWgk6AAKL/UxDENjqRjr/YE+4gfO2l0XKoMrCZzd0leB88Z7j1d9fnQ6q7n8yi21YUNeUGpmDWfZdjSTLVVVOEeSUY0mo8H02o1iSYVzjVtq/atLc/myvnCX+3vfvUyFU3K3rrnr6dmOTRXzW2qXW8MpSR/8xUt14eSQJOnQVFZ/9O2DettXHlzxypi/lUq+RMsGAPRS2XKCk8xjM/ng9vCAwEydC9XhfTXn8mUlY6b8YkntkLuRRKTp+REA1p6fJ82a07zaLjusvb4KnIfOZas+PzqTC64WLjc0SJJecckWXXfxlkqFs4mW2plsUY4qbbS+XWPJYH/OjSIeCQXOUveGBkmVanLtGs5aV+0aU65k63CH2mrzJVuxiLFkMXmt6w5s0d+9/koZkh47Uxk4cZs32Krxz3dPXpr5WwQArJ2y7SgRNRUxqtdthfdYni8srU6GKyBzuZJSsYj2bU5rKB7R7167r+q+I4mY5vO83gP9omFLrekPDaIg0C3Lp7guyRTL+q0b79epmtbD43N5XTA5pKF4JBgy08gf/8KlkqRZb/1EMy21/jqOySWBM6WDLU6yG3T+tNhcyerSGs7K7/PR0wuStGxLrVRpd55aLAYVx9UolK2m22mHE1Ht25zW/V67tyQ9cS6jl1w42fB7it6JCle8AaC3yrZb4YxFzOC1WZKyocC5kC9LY9XfVwxVOMu2o2TU1Ggyplvf9sIljzGSjDA0COgjjabUsi1K9zVd4fzEJz6h17zmNbrmmmv0vOc9T295y1t08ODBjhzE7Udm9chpN+Bdum04uH02V9JcvrRidTPMHxrUzEm+PxhoSYVzPKkTc/ngD3Uj8N9Uz2WKsh2teUttPNTGemQ6p9FkVCMr/J79SbVnOrQ1Sr5sLzswqNblO0er1v6cnG/uOJpdTwwAWBtl21Y0YioWMauqGuGWWr86OZstBes5izUVkMQy740jiSgXGIE+Yjn1K5xBSy0Vzq5p+mz7jjvu0PXXX68vfelL+sxnPqNIJKI3vvGNmp1d3RCXB0/O6z3feDj4/Pn7NgUfZ4qWzi0Wm16/KblrAxNRs6mT/EdOLcqQtGeiurK2eyypsu3o5PzGaav1A+cJr5V4KLG2xe+oaehf3vp8RUxDjlZup5U6v2VNvmQpucL6zbDLd4wofA3i1DJ/H05o+ESzE5MBoN/ZjlP1+jYoSpZf4TSqqhrhwLlQKGs2V9LPfPxH+sRthyUtDZypZd4zRhJRWmqBPkKFs380fbb9qU99Sq95zWt08cUX68CBA/rwhz+s6elp3X13a3taLfm5Pz4qSbpm95g+9yvX6OIt1a2SR2dyTU+o9Q0nok2d5N9+ZEaXbh+p2lNLki70juHxs5l637Yu+YMRDnprFLePJJa7e0eMpWLBHqortdNK7hYlo8moziwU9LX7T676SnKhbC/Z9mQ520eqQ/FyFc7wBQ8qnADWi9+68X695tN39vowWua31EZNo2GFczpbCgLjtx87K6m6pVZaulVW2EjSrXAOYiAH1qNG+3D6y7qYUts9bQ8NymQysm1bo6OjqzoA/8X8/T93QAe2DgfhctRrrzy1UFh2D856huKRFU/yM8WyHjw5r+fsGV/ytQsnh2Qa1QNi1ruC9wbsP/d2j68cADvB/z0vtwdn2ORQXLc+MaU/+efH9aF/eXxVj50v2ytOqA3bFNo+56ItQzq9UGh4YhGuwtJiBWA9sB1Hdx+b09Ozg9f940+pjUfNqpPM8BrOj/3bU5rJFoP7S+4J6VBopsFyXTEjiagsR8oxmRzoC8G2KEuGBlHh7La2+yY/8IEP6NJLL9XVV1+94n0NQxofT9f92nzR0ssv2apL9rittC8fS+mPi5YmhxN6y+fd6unWsVTD769nPB1XwXaW/Z6Hn5yS5UjXXrK17v32Tw7rqZlcS487yJyaJ+OleyZaqv61a/NwQk9NZXXRjtGm/lvvGE/p0JPudNgnprKr+v2UHWk4GWv6Z+wLDRh6xs4xPX42o1I0oq1e5fOpcxkdn83pOXs3afZ05WJFyTB69ncUiZgb5m8Y6Dfr7fn30InK0LRB+3cZEVOJWMRd02VWfi+O97r+R7/0TL3vGw/pdM69QGjL/Tc6pru/ZsarhI4PJxr+27dNuLcbiZjGm1gmgrWz3p57aE8i5S7FGq/JEf7azWg8yt9Jl7QVOD/4wQ/qrrvu0he/+EVFIiuHEseRZmezdb92bqGgA5NDVV9/xYWb9cS5Sjtrwmj8/fUkI4ZmM4WG31O2bH3noZOSpL0jibr3O7AlrX87NK1TZxe6Erx6bTFXPVkvnymoG9ew097V4omY2dTveDJdqTJOLxY1M5ORYSy/rUkjmXxJm4fiTf9tGaErYdfsHNHX75P+6b4TeuVl2yVJv/LpO3R6oaBnbh/RZTtGJLlXw6fm8y39/XbS+Hi6Z48NbHTr7fn3o4Nngo+npjMrbinVT3KFkkxJjqRsvhT8Xqbn3G22RrwhIien3duLZVuzs1ll8iUlIqYipiHLdmTYdsPfacTbbuX4mQWlHKqcvbTenntoz4I3ZDKTyWt2tnIu73enLSyTFdCeLVtG6t7eckvtn/zJn+iWW27RZz7zGZ133nmrOijHcTSbK2kivXSN5nhoUFArQ4Mkdw1nvZZay3a0WCjrkz86os/eeUyb0rGGk1F/6fLtms+XdfNDp1t67EFVsGyd12Rbaye12lL7otBQqZlcaVUDhPIlu6WhQeGTq2fvGdeO0YT+5WBlnc/phYJ2jiZ0eDqrL99zQqPJqHaOJWmpBbAuLIRey8JrHwdB2XIUjbjbopTs6jWchqRxb+mOv/e3v1dnoWwrHjWDvaOX20rL3wd8gdd8oC802ofTMNz13LTUdk9LFc4//uM/1re+9S3dcMMNuuCCC1b94IsFS2XbqR84Q0FwouXAGdFinaFBb//qg/rxkcq2Fv/luXsa/oyrd43pyp2j+tvbDuunL57UpnS84X3Xg2LZ1o7RpJ6/d5PO39Sd9ZuStCkdVzxiaNtIc4EzPMVYkp6ezWnLcHsDjvJlq6U1nGEjiahecclWffbOp3V8LidD7ovZrz/vfJUdRx/858dVKNveAKvBOjEDgHrCF3IXCuUVt7LqJ2XbVtQ05DhasoYzHY8o5a3TnPOGBlXWcNqKR9xp6pKW3UrL38JtJsdenEA/aDSlVnK3RimxLUrXNH22/f73v19f/epX9Wd/9mcaHR3V2bNndfbsWWUy7U9ynfYW54/XCZTRSOXQXrh/05KvL2e4zl5Y8/lS1R6Kb3zueXrdNbsa/gzDMPTun75Qc/myvv/EVEuPP4j8q7jvfvmF+k9XN/7v0mnXP2uXPvraK4IF3CtJRE19+g1X6WOvvVySdHwVwytanVJbexyvvWqnDMPQV+87pbNe28aWkbheduFmSe7Jx2gyqsPTWZ1e6MzeoQDQK+Hp74PWueFPqY1F3X04y5at6z72Q33t/pNKxSJB5XIuVwruL7kXY8P7RieWqXCevymtyAYbOAj0s2AfzjrnmFHTDAIp1l7Tlye/8IUvSJJ+7dd+rer23/md39Hb3va2th581nth31SnwilJH/zFS3XeRCpoU2nWUDyiXMnWXU/PqmjZunjLsO4/MS/bkbYOx3VmsaiLtwyv+HMu2DKkiFHZm3I9K5Zbay/tlM1DcW0eaq16fPnOUZUtW6YhHVvF7yZfam1KbZhhGNo2ktD5Eyk9PZsLAuXW4YQm0nF98Bcv1f7JtKYzJb39aw/q728/qt+/7qK2jxUAei0cMgetbbRsO0pGIzIMKVd0NF8oB9XMLcMRpbzKZVDh9AOn5WgkFtHvXrtP//O7T2rnWOOOmlQsogu3DOuB0HAlAL3TqKVW8iucBM5uaTrJPfbYYx1/8OmsGzgnUvUDx3UHtrT1c/2A+pYb75ckPW/vhPZuSisRNfX311+tz991TC9qomoaNQ1tG03q5Pz6D5wFq/oqbr+LRkxtH0no+Gyure93HEf5stVyhfN/v/5KPTlVWWA+noppNlfS2UW3Wr/Va+/1/3b3b5Yu3zGiR05zxRvAYAsvDxi0/YX9NZym4bbRhdegpmOR4L3AX8PpK1q24hFT/+nqXfr3l+9Y8SLl5TtG9K2Hz8iynYEaqgSsR/YyFc5YxFSRltqu6WnC8CuH20baW4PXyHC8kqOv2jWqh08t6MlzGe3fnNbWkYTe8dILmg4aO8eSG6bCGY8MTuCUpJ3jqbZ/N/myLdtxTzRaceWuMb36ih3B537gPLNYUDJqajix9OddvHVYT57LsDgdwEDLFMraOuxeIB60ltqSt4YzFjFUsh1lQoE5FY8EQXIuV/3vCr83NtMRc2DrsLIli2UUQB9YrsI5nIgM3OvYIOtKwnjwxJy+et+JJbcfmspoUzqm8QYtte0Kn/S/7KJJzefLuvPorPZPDrX8s3aOJnRifv2/cRTK7beX9sq24XhQWWzVvNc2tdqhF+OpmOZyJZ1ZKGrrSKLuFi0Htg6rULZ1eJrR2wAG12LR0vZRd8DbQqGst33lAf3q5+7u8VE1p2w5ipqmO5nSsqsGCw7FIzINQ4moWVXhdBzHHRoUbb5SuXvcHbp3fK697hsAnVNeZmjQSJ15L1g7XUsYn/rx0SW3HZrKav/mzm+4OhRa83n5jtHg4wvaeKydY0lNZYrKlwarfahVRWvwAudwIlp3GnEzFrzAOdri+uBa46mo5nIlnV7IB1f+ax3Y6q4XPsggCQADLFO0go6khUJZPz48MzDLBcq221Ibj5gqWk5Ve3DK63RJRt2v+QplWwXLaan7x9/iazUD7QB0ht9YVi9wDieiWhiwpQGDrGsJo3YKqeM4emoqq/2bW686riQ8ZOiiLZWfv6/NwClJJ9dxldNxnIGscA4losoUrKBHvxXzBfcq9mornGOpmCzHvXjSaHuW8731w0wuBDDIMoWyxpJRJaOmDp2rTKgPvwb/5Ois/vstjwQbq/eLYEptxJ1SG564m/a2RKldapMtWd62KM2/N24dTihqGqsaaAegM/yW2nrLqUeTUS3k2cKoW7qWME7MF/TpUJXz7GJRmaKl8zd1vsI5HK+8aSRjEX3+V67R9c/apZ86b7zln7XTax86MZ9ft6V3/4ruoK3hHI5H5Ki9DciDCmcHWmol98r/1gZrkaOmoQsmh6hwAhhYjuNosWhpKOFu93TbU9PB1+a9dY+ZYlm/9Y/3658ePdt3e1FWAqe72Xt4Dae/lj9Vs8dmtmgFW4Y1K2Ia2jmWpMIJ9AE/cNbbem+ECmdXdTVhfPy2w8Emq/6+hdtHOzswSKpuqZXcoS2tDAoK8yuc3zt4Ti/76A/1vcfPdeQY+0mh7D7hBmlKrVSpZLdzIWC+Q4FzIrT+uFFLrSQd2Dqkx85k+u6qPwA0o1C2ZdmOhuMRjaViypUq0x3PZYs6NZ/XdR/7UXBbvw3NKVu2YhFTUdOtcIbfN1J+hbNmj81s0a9wtjZtdudoUic2wHR7oN/5+3CaDVpqFwvltrrk0LquJIxw5cy/6lfZRqK1PRibMeIFkYu3rL5dd/NQXPGIoa8/eEqSdMeRmVX/zH7jnzi0OrG114LA2U6Fs+Cv4VzdwCq/wimpYUut5K4lXiiU9ShVTgADyF/zOJSIaqzmQt3UYlEfv+1w1STuM/0WOL0KZzzq7r0XXsM51KDCmSlasp3WL8ZODsc1lWl+oN2bvnSv/uDmR1p6DAArs2xHhiSzzkDHkUS07S45tK4rgfOircN63dU7JUlHZtzJbWe8wDm5zEl6uxJRU//r1Zfpo6+9fNU/yzQMTQ5VQvFsbv211fpPtnR80AKne7yZNiuchqShOtuYtGKH13ItqWFLrSRde8FmSdKvfu4efffg2VU9JgB0m98iO+RVOMOmskU9enpRL7lgs/7fW54nqQ8rnH5LrWmqbDvBRUepUuFM1Fx09SfWtrrcZFM6pulssamOlmzR0j3H5/XPj/G+AHSa7TTeD9ef4eF3vGFtdSVwGoahN73gfEnS0Rl3a4hzmYIihjSR6uyWKL4X7NukiXRnqqfz3huTabhbuaw32dKABs74Kiqc+bJGktG6V71aMZ6K6fpn7ZIk7R5LNrzfWCqml188KUn6zsH115YNYH37vw+fkWlIV+4a1VjSfd++YNKdwXB2sajjc3ntGk9qIh1T1DR0eqG9LavWStmyFY0YinrtseH9Nv0T0mRNJXPOOxFtPXDGVbIcLTaxPuyeY3PBx7N9tu4VGHSWvUzg9LrkFtbpfJZ+s7oFbC0YTcY0kYoFFc6zi0VtHoo3/EPoJ3/4c5fo8HRWs7myvnDXMe+Na7DWOy4n603rSw1oS207Fc65fCl4sVmtd7z0Ar35BXtXDOx/9POX6OT8fZrO9teJGACs5NuPntGL9m/WrrGUxlLua+eO0aROzRf0yOkFFcq2do0lZRqGto4kdHqhf9Yw2o4jy1EwpVaSZnOh12GvEum/B0ZNd7CQX/mItdhSu2nIDeRT2eKKk9DvP1EJnAfPLOo550+09FgAGivbjiINCgsjq5gDgtZ1NTVdMJkOJnWeXSwsu+atn7z4gs36lWefp32bUyrbjk6ssy1SskV3DefQoFU4vXbYdl4sFgrlVQ8MCmumOhyLmNo9llzXW+wAWJ8yRUs7vCF/foUzETW1f/OQbvWG6e0aT0mStg3H+6qltuxNYo9FTMW8i9zh5TF+42vSW8PpvzfMZN2KY6vzDTZ53VX+9y9nJleSfzr8xLn110EF9JLt1N+DU6q01C7QUtsVXQ2cl+0Y1cGzGeVLls4sFrVlDQYGraXzvDfTp2dzPT6Szsp5LbWDWuFcLFhyHEe/8cV79a6bHgr+PY08cTajnxyd1f7Jzu8Bu5IdY0mdXigwFQ3AQCmG9qP0A5khQwe2DsnLc9rlLSvYPZ7S0320LUg5tDWCX60Md5qMegHan9fgn6DOePdp9b1xsxc4m+lmWchb2j3u/nfLMLwE6CjLduruwSlViiyLRQJnN3Q1cF6+c1SW7eihUws6OZevGrgyCHZ7gfPYzPoKnH5L7aBVOJNRUxHDfbE4MpPTfSfm9f0np/Sth083/J4zCwX9xpfu1VA8qt958b4uHq1rx2hCZdvRjw+vv2nHANavkmUr5q1/9AOZabjbjvn8favP35TWVKbYN61qZdvt4omYRlDhnM6W9HOXbtX7f+6ArvPW1//UHnevbn+KfnhQUiv87bKmMitXOBcLZY2l3HWvhbK94v0BNK9QtpRo0BLvr9nmedcdXQ2cV+wcVcQ09KkfH1XeW+8xSDalY0rHIuuuwpn1tkVJDVjgNAxDQ4moFgtW1XY1dxyZbfg9j5xeVKZo6UO/dGnV9OFu2e6dkP3Xrz6oOQZEABgAlu3IdhSsf/SHrSVjpq7aNSZJesdL9wfbh+yZ6K9uoEqF0wz+DZJb0fz5Z2yT4f17Lt8xWvV9/tYmrb43+ttl/c/vPqFTK+zHuVAoazgRVSJqcuILdNh0ttRwgGjS61zgedcdXQ2c46mY3vic83TnUTcQ7BofrMBpGIZ2jyd1rI9ahTphUIcGSdJYMqq5XEl3HJnVzrGkfumybfrJ07Oy7Potq1MZd13R7rFUNw8zcM3uMe3b7E52fPDkQk+OAQBaUbLcEzK/pfZlF03qNVfu0G+/eJ/2bU7ru7/9Al3/rN3B/f3AeXS6TwKn1/MbjRhBlVaq3kdZcgP1e15+oT7y75+pRNRsew1nxDT04v2bJEmPnl5+7+WFQlmjQeCkpRbopOlsSZvS9XfD8Cuc+RKBsxu6Pmr11VfuCD7e1aOT/tU4byLVN1dtOyVbtJWKmaveIqQXNqXjOrtY0E+entVzzx/XlbvGNJ8v61iD39FUxh3Q0OgFaK2lYhH9w/VXyzSkB07O9+QYAKAVRS9w+usfE1FTv3/dRcFwnNpJrLvHUzIN6anpbHcPtIGqNZyhCud4nfeB1161Uy+5cLOSUTNoqU3FWj9Vetu1+yWtXD3xt+hKUuEEOm46U2x4vheNuMuyuNDTHV0PnOHJtP7Eu0GyezylE3P54A1sPciWygNZ3ZSkTUNx3XN8XpmipefsmdB+r3p4uMGJzrlMUeOpWE+3tUnHI7pwckgPnFgaOM8tFvSKj/9I/8Im4AD6RNGrEMYjzV2UTERNXTA5pIdO9UcXh1+hja1Q4QwLt7gOxVufaO6vGytYjUOk4zihltoIgRPoIMdxNJ0tBhfG6knGIsrzvOuKnpx1v/qKHdqUjgX904PkvPGkyrbTV3uMrVa2aA3cwCBf+MrVNeeNae8mN3A+NVU/cE5l3P1fe+3S7SN67MyiHG9are04+tHhab335kc0nS3pOwfP9fgIAcAVBDaz+VOGy3aM6MGT830xkTu8hjPcWbVc4Ayfn7RT4Uw0MZAkX7ZVth2NsIYT6LhM0VLRcrRpmXM+nnfd07mNCFvw3p+5SO/9mYt68dCrVplUm9eusZT+8tZDev7eCT137+Bu1pwr2YNb4fQC53AiElzF2jIcb1jhnMoWezIsqNaBrcP6+gOn9M0HT+sbD57SfV61M+pNUHTU+5M0AJCkYtlvqW1+2cXlO0b1tftP6amprC7owRZUYeGW2t2h2RHLBk4vMMYjRlsdMc0ETn//v5GkGziptACd4w/9Wm4JVTJqKr/CVnrojN71FQ6o8F6c2aKlz991TL/zlQd6fFSrky2WB7jC6YbH0UTl2sneTWk91WBYxbnFojYP9Wb9ZtgBbyuBP/r2wSBsPmfPuG5583P1nD3jfbVpOoCNrRS01DZ/ynC+123SXMBpPgAAIABJREFUD69l4cAZnlUwnmp8zd2vcLZ7MbYSOJeezPrHs+BtGxNUOBleAnSMP/RrucBJK3v39KTCOcgmh+NKxUzdfWxOl+8cXfkbBkC2ZC/7xtvP/FaJoVDg3LcprVsePi3HcYJx95LbtjqV7Y+W2ou2VK74v/dnLtJVu0a1ayylRNTUtpGEbj/CPp0A+kPJ9tdANh84095FzGyx99WDstcSHPXWb54/kdKRmZyGE8sETi8wtnsx1g23leqw755jc3rTl+/T7167LwieI4mIElFTsy1ulfXYmUWdXSzoRfs3t3WMwHr2yBl3QvTkUON5MckYnQXdMpgpo4dMw9Drr9mlv7/9aW0ZrgSXTLHc1mCBfpAtlrVzAAc4SVLaW1sTPnHYuzmtTNHSmcWito1U/l1nFgoqWY52jfd+OnIqFtHHXnu5zmWK+neXbA1aaSVp60hC5zJFlW1HUdPQuUxRh85l9Ow941UBGsD69tDJeU0OJ6pex3rBD03NDg2SKkEt42271UvhCqck/e83XKWnZ3LLTmYPKpxtBk7DMOq2yf7fR05Lkv7qX58Kbts+mmyr0vLLN9wtSbrz965d8rX7js9p11hSk8OD+d4OrEa+ZOkTtx3Ws84b0/7JdMP7bYRW9v928yNKxky97xUHenoctNS24Q3X7JIk3fzQ6eC2x89kenU4q5YtWsHV6EGzb7NbKXz91Tsrt3mtXIdrBgcdmXHbbM+f6H3glKTnnD+hn3/GtqqwKbmB03bcibWS9L++f0i//X8e0C9+8nZ94a5jevDkvN5y43169HR/TIAEsDZ+7Qv36jWfvrPXhxG01LZU4Yz5gbP3FU7/hDIZdY9pPBVbsUPJr3C2ugdnWL0QeW6xuOR+ezellYjVH15Sth3ddmhaT5ytPscID2Pyq8jHZnNayJdlO45+40v36de/eG/bxw4MsqMzOWWKll575c7lLyxFIyp0YQ3nU1NZvfnL92k221oXQyd8+7Gz+saDp3u+VpXA2YaJdFwTqZjm85Urt8fnBndqbbZkDezQoG0jCd35e9fqpy/eEty219sapXYPuKNe4NzTJ4GzkT1eBfbGe04oUyzrYW9rge2jSf3FrYf0xi/cq7uentO/PjnVy8MEsIb8NtB+WF8U7MPZQuAc6qOW2px3DK1UK5Ne98xqpunXm4D58OnFqs+vf5Z7AbvRPpz/eO8Jvf1rD+oNn71L33jglAplW3O5UtUk9hPe+cerPnWnfu0L9+iMt272xHzv188CveCfk4eHhNXTrQrnP957Qncfm9P/ue/Emj9WWLhN/8eHe7tUi8DZJj/UvHDfJknSmcXBfGF3HEe5Ad4WpZ7N6ZhGElEdns7qtkPT+qdHzkhyA2cqZvbFlNrlPOu8MT33/HHd8JNjeu2nf6KjMzm99UV79cnXXakLQ9MeTwzwRQ4Ay5tpcT3fWvK3RWmlpTYaMRWPGP0ROL0r+61sb3LlrjFJ0sEziyvcs7FE1Kxaw1ks28HkTEn669dcpt+9dn9w39rAadmOvnTXMe0eT+qZ20f093cc1Ye/87iu+5sf6dYnKltnHZ/LBRXPozO5oJsH2Igs29GxWfc5EN4GqZ5kg86CTvOfnz95enbNHyvsaOi14N7jS/d+76bBXHTYBxa96XI//4ytevDkfF9M4mtH0XJkOe1P4utHhmG4k2qnsvrKfSclSS+7aFKHp7LaM5Hu+3WQhmHoI//+mfrXJ6f0iR8ekTLSlbtGFTENffr6qzSdLer9/+/gQFfVASxvOlMJnPmS1dN9q4tttNRK0lA8qmwfbDlQCZzN/zf8xWdu093H5nTFKoYD1obI2v8WV+4aU8RbUuHet/rrZxYLOjFf0Huvu1CmYegD//y4js26r/t/e9uR4Ocfn8sHW6xI1SeZ/eLcYkE/PjKjX3zm9l4fCho4lynqJ0dn9bOXbu31obTt356c0jtvekjP3jOu0WRUI8nlY06iS9ui+M/J+0/MB/M5uuHojNsJMZyI6LGz7V886wQqnG36rRfu1Y7RhF64f5O2jiQGNnBmvYEO6QEdeNTIvs2poBVVkn50eEYPn17QJduGe3hUzUvGIvp3l2zVZ3/5av3lqy/T1d7V9lQsol1jKe0aSxI4gXVsKluphJ3scWtkpcLZ2ilDOh7pizWcOW+7kVbWY5qGof/xswf06it2tP24SwKn99/id6/dp0++7sqqAJyImrKcSiu1JE171dAtwwm95MKlk2iv3j2m4UREx2fzmgsFziOh5SS9Xrfle91n7tL7/9/Blifxonv+4OZH9L5vPapzmaXrjAfF399+VJJ059FZ7Rpbvp1W8tZwdrDCefex2aAgFeYHzpJVqb6utbJl69uPnlXENPSyCyd18MyiHKd3e7wTONv04gs26xu/+VwNxaPaNpII1kwMGv+Kazq+vv4U9m5KV/Xl33jPcc3ny7pix2BtZTMUj+qF+zYtqcruGkvq7GKxb04mAHTWdChwdusEpZFSsIaztavy6XhEmTonX92WK1kyVNkbs1tqq5Z+4NwxmtTVu8dq7uuGz/D71pS/j+BQXBPpeLCfoF+Bes0VO7QpHdd0tqS5UJD76v0ng4/P1BlS1G3nFgvBzAsCZ+89dHJeb//qg0G790y2qDMLBZ31loadHNCL2WXL1qHQ2ub9mxtPp/V1cg1npljWm798v/6/bzysj//gKX357uOS3Is+pxcKuvYC96LRoZqBlmvltqem9aPDM3rzC87XM7aPaD5f1qkeZpX1lTJ6ZNtAVzi9wLmOWmolaV/oheb8iZTuOOr2za+XvVPP8wYLsVYHWJ9mQtMMHz/b2yno7bfURvqmpTYZM7u+nCIeMVWwQtNkgwu8S99v/TAcrrb4Fc7NXtAcS7r///y9E/rRO16sl140qdFkVAuFkubylb+XkuXoQ6+8VJJ0eqH34eGup+eCj3sxpRPV3vPNR3TbU9N63Gux/Hcf/7F+4ZO3BxX3Qe2eOjqbq+qoeFUT3Qn+Gk67QeVvsVCu6jpYjn9R5SdHZ/Xp25/WR773pCTpxLz73/NF+92ZL09Ndef13P89vvqKHTqw1e3ue+x079pqCZwdsGM0qbl8Wb//zYd1+5EZOY7T8I+3275z8Kxuffxcw68HgXMdDQ2S3FajX3jmNn38P16hK3e5IXM8FdP5m/p7Qm2znrF9RJJ7pRLA+jOVKSkRNbVnonp5QC+spqW2X4YG9WJOwdIKp3tCWm9IX93A6YWzibQ76G444X7f5nQ8WAM2kohqPl/WXK5SSd6UjgXLR47P9j48PBB6n6LC2Xv+et/Hz2b0F7c+GdxeCZyDeSH78LR73L/1wr26/lm7mlp/7XcWFBtUOV/20R/q3d94uKnH9wNn+OzfcZxgScT+zWltH0noyHR3/vuemi8oHYtoNBnVRVuGZBrSY6sYgrZa62vhXo/80mXb9Hc/OqLvHDyn7xx0w92L92/Sn7/qsp4e1xPnMvr9bz4iqf7G0FLliut6Ghokua2o/+Nn3U1uH/WeYO4Trr8HBjVr93hS46mY7j+5oFdf2eujAdBpx+dy2pyO6RnbR3RXlycb1vJPxlpuqY1FdazYu8Bzcj6vN33pPp1aKDS1nqvTlg4Ncj+u936brBs4ixpORIIw+vvXXaQ/+96TVZ06o8monp7NVVU4J4fi2j6SVCxi9MUAoftPzAdzBwicvZUvWcF531fuOxmcH0luS6jUHxcp2uGvXX79NbuaLqL4z7t82V4ymM0vHP3g0HRTPys8uMs3nS3plFfh3D7qnrctdGmZwamFgraNJmQYhpKxiM6fSOtgD7tlqHB2wEQ6rn+4/mp9/D9eoVdd4U5g+7dD03r0dG+vSn/zwVPBx7kGbU3+/mRD62xoUNgWbxuUS7eN9PhIOscwDF2+Y0QPnKDCCawn7/76Q/rPn79Htz4xpZdcOKlLtw3r7GIxWF/VCyWvLTTe4hrIoURvK5xfue9ksGapFxdVaweSVIb0Na5w5kMV0elsSZvSlW28Lt46rE+87sqq7x9JRLWQL1et4TywdVgR09Du8VTPA6ftOHriXEbP2zshiQpnr4Xbmx+tqXY97f2t9HrNeLuemspq63C8pY49/771Bv2EX7saVUDD5hsMCzo5X1DENDQ5FNdwIlL3sdbCqfm8to8kgs8v3jq0qm2eVovA2SEXbhnST+0Z1x/8zMX63u+8QOlYRF+463hPjylcOv+/j5ypO50qqHCus6FBYS+/eFLveOl+/ebz9/T6UDrq8p2jOjqT4w0cWEdufWJKD59aUCJq6nXX7NT/z955h7V1nm38PtoLkEDsvQ0GL2zs2I5X7NgZjrOHs9rs2aRpm69Nm7RpOpKmTdvsNHs7y0kcx3ZixyPx3oBtzDB7CoEQ2vN8fxydgwABEkgM+/1dV64rYEkckM457/M+93PfUz3y+VNt47dQsLvc4POogBUi8nGW1Hq7tY6XpNbuw6XWl6SWlc12ec04dpntnFHQYDAznE50W5yIkAjwm2WZ+PWyLACMf8F4F5ydJjscLhoZUXKIBTx0W8bfROpcZltlBxRiPlbkRgMAIiQC/PliRg3GzmpXaU0TZiwsEOq6zH38O/whytOQ6PThzOt97fJHimrwUhlkRzOZ6fVdZq7w4/MoyEWCMXPubuuxIT68V9mRqJRCY7TB5R6f9/bsrTLGEYVYgDWFcfi+ogN1XeZxcRKlaRqVGhMWpDNDyn/fWoXPjrcOeAxrdiQXnr0dTgGfh7VFSeOaYxcK2PmEE2SOk0A4a5AJ+bisIBZb7pmHxAgpcmMU4FHAqXFUzNhdbogClNMCQIxCDLPDhRd+rPHbeCNYvLK7FjurO7mvAxw/DQqifg6Y7ALWV/Ebo2AWvq/ursO2ig4ATBard4fTF+ESIdw0k7cXKRfh2pm9csIUlRSN3ZYxCbYfDHZ+LSFCDKVUiG4r2SAdTw7W6zA/LRLXzkgAwEhJVdLeTY2MKBmMNheX9zpZoGka9V0WpEWOsOD0YWblXXA2+tH17fGS1C5Ij0SERIDjLT1o7bEhPpzpNMrFY+PcbXW4oLM4EBfe2+GMkongpgHdODUpSMEZItYWJYICcM3bh3HnuhLOdGGsaOmxwmBzYlFmJK6byVxYXt5dyx0HTdP44+YKvLqnHgAgPctMg84F8uPCwKdAZLUEwlkCTdOwOV0e6RWzCSgR8pERJR9X4yCniw7YoRYArp6RgCunxeO9Q0345FhLCI7MN06XG28daATAmMUBGJc8UHaGk1UXmR0u8Cnf8SxqhRg8ipE5/m4j473gT4eTDbY/0qhHllre59/OS4uE003jrf31wfh1RoT3/JpKKuwj/SWMPWaHCyqZENMTw3H9rET8/dI8qKS9mxrzPU2K8R4JC5QOox1mhwupARacak/BqfURH8TOtALwK4mCnc1cnqPGzXOSMCdFiZ1VWpS3G5DjcYlVjFGHkx0liPWS1KoVg3dzxwJScIaIuHAJ/nBhDgDmBvJ1WdswzwguFRpmMDg3RoFfL8vC06vzYLK7OP32qXYjNpdruMePZPeaML5IhXzkxChwtEk//IMJ5wRdZju2DCKfJ0x8nG4aLrrXOZGlMIGZ13aOkxTK7nKPqOAUC3j43YpsJCslKBnDjTG9V6eBldiNh7S3vxGQ2e6CTCTwGc8i4FF9XIAdLjf0VufwHU7PxgQNICe6b8E5O0WJxZlR2HCifdhrwvYqLbQhmBNmO5zx4UyHc7wWuwQGu9MNsYCJCPrV0kycnxkFldemxpKsKIj4FMrHMT5jJNR65PNpASYRKKVC8Cig0+yr4Oy9ZvhTcPZYnVBKhfj76nyES4QoTlXBZHfB4aJxQQ4jYZZ7ZjhDfY9u5867XkktG6+kJQXn2cclU2Nx6FeLECkTDhjODjUVGiP4FJDp2fEsjGfkl6WtzK7VDxUdEPAorCmMQ26MYszzyQjBoThVhbJWQ5+dOMK5icPlxspX9uPxTafH1fqcMHKsHhdTibDvrbk4hVm4lI9Tl9MxQkktS26MYkw/k96SMdbIbzwKTlaupzHacaBeh26LA1Lh4Msub/lttZbZNI6U+9fhBIBcTxSKN8WpSmhN9gGB7y/8WIunvqvAtyfbsfp/B/B/G07hic0Vw/9SAdLaY0W4RAC5SIAkpQQNOgvZEBsnaJqG3UUPiDdSeklqpyWEIytagXKvDuemU+342YfHJvRcJzuvnR5gh5PPoxApEw07w6nxp8NpdSLc63y8KC8Gy3PUKIwPR0E8M4svFwngohFymXsrpyyYOB3Os3dwbwKRMg6D+5UaI1IjZdzcYkyYGLFhYpS19OCGWYnYX6/DrKQIrgtLmJzMTVXi3YONONygx+KsqPE+HMI44n0T6TQR2dpkhHUolfSTXM5OUYICcLBB1ycSY6ywOQcuUgMhJ0aBbZVaGKzOPgVSqGBlmy9fU4j0KGbT1TwOXgpsd+GdAw345mQ7ACDBawE4FMc8ypXhZzh7/56+nNjZz8tre+qgtzrxyyWZSFFJ8d4hRnK84UQ791h/FtWB0m6wcbK+9Cg5THYXNEZ7H6kfYWwYzG2a/XrllGhQFIW8WAW2lGvgpmnwKAp/9GxEdEzg961CY0S4RMBt8gRClHyQgtNzzUhVSf3ucIaJe89HiZCPv6/O7/MYNkvXaHeF1FekzWADjwKiFX1nOAEiqT2rGeuCU29x4FSbAbkxfXc7c2MUqOlk3McadBZk9ZPfECYf0xMiECkT4svS1uEfTDirMdp6F9Q6C5GtTUZ6O5x9FyJKqRAJERLUaJldfKPNOaZOgxaHK6Cogf7kRDP3oprOscmAY527lVIhZ4iyZBw25NjuAltsAkBLz+AL10WZvcd4tJEtOIfucKZHyfGz4mS8vXZGn04VS7ZaDoWYj29PabC7pgt/2nx60NcShGC0xrtIyVQz3aex+hwQ+mL3eHj4miHe+/BC/PniKQCAvFgFTHbGOMi7G92gMw943kSApmkcrO/GrKSIEan1ouTCQWY4mXtqepQMGh//3p8e2/AbamwEYaiNg9p6rIhWiCHg9f49JEI+FGI+KTjPZlJVMnSa7GOWvfPXrVXosTqxMi+mz/dTVFI06ixoN9hgc7qRqgpM606YeIgEPFwzIwF7arvwweGm8T4cwjjiHSat8+G4R5j4sDKr/h1OAIiPkKC1h7G0X/36ATzy1YkxOy6z3TmqgpM15hirzyVbcKqkQvB5FDbfMw9/XJU7Jj/bG+9u0C+XZOC+hWn41dLMQR//t0vzsPmeeZAKedxs/nAdGwGPwv3np6Mg3nfnW8Dn4b9XFmJRZhSWZatxqs3QZ8H5fxdk4ReL0iHkU2jqtgZdNtlhtHHvf4Znnra2c2IWLmc77PXF1zy2kM/jYo/YTnl5m6GPFHu8I3YGo7HbijaDDXNTVSN6fmaUHNVaE3r6OSizRWGGWo5ui2NYwyuD1cHNVA8GG4lkDLHEv81g65PByRI1iHx4LCAF5xiQ4ins6sfgZKVpGseb9FiVF8NFongfh91F41B9t+frwLTuhInJTbOTsDAjEi/vrkWL3oqtFR0TetaCEBpIwTn5YSW1/U2DACA+TIw2gxXl7QYYbS7srdWhpHlsDMNMdteociwjpMwirNvigM3pxsaTbSF1bmcLzghPx08tF43I9Gi0eP/M89Ii8fO5Kbh+VuKgjxcLeFDLRUhVybjzWTVMh9MfpiWE41+XT8WlU2PhooGd1VoAwF8unoKrZyTg5jnJ+PXSTNicbix7cS+e3lY16p8JMG7BOrMD0Z7ZMZVMBKVUyHXqCWML1+Ec5lzIiJJxxkHHvEwJJ2rBecYz78zOSQbKBTlqON00fqjU9vm+2eECjwIWe5QHu850+no6R48fIwNyj6Q29B1OW5/5TRa1QkRMg85mWOOe6o7QmyZoTXboLI4Bclqgt/D9qaazz9eEyY1EyMfP56bA4aKx5o2DeGxjOf76fWVIHAcJExeDlzNnF4kemJQMZhoEMPOAWqMdu2u6uO+tO9qCO9cdxw+VHSE9LovDxe3MjwRW6tltcWBPTSee3FKJv35fGazD64PN6cb+Oh3kIv64FJmDEYh7ZqrnsWIBD7Igznmx5oFPb6sGwHg7cP+WEA4Rn4LJ7sIXJa1BcUTWmuyg0XeOLCNKRiS144Td0+HsP8PZHwGfh+xoBU5rDDhQr4NSKkSWWo6PjjRje4ivNSOB7UxG+JCU+0N+XBiy1HI8u70aB+t13PfNdhfkIgHyYhVICBdjR5V20NegaRpGW1/TIF8oWEltCDucbppGu8GGOC+HWhbS4TzLSVRKIBfxuagSu9PNZVMFk9YeKy557QAA+Cw4WQntzupOREgE3K4jYfJTEB+GZGXvxWXDiXY8u/3MOB4RYaxhOyJxYWJ0kw7npGQw0yCAmQekAby5vwGF8eHIiJJhW2UHjjf3YItXxFUoMNlHN8MpEfIhEfDQbXFykSXfntL02SQJFn/9vhLHm3vGJXfTF69eOw3/ubIgoNmyhAjmWl4YHxZUB3mlTIhfLsngvo4J610DZEcrsOsXC/EXzxxfMByR2U6K91qDKTjNxKl2HGA7nMMVnAAzx3m63Yj9dTrMSVHigfPTAQDbKgcvusaLHs91JGwYOetgUBSFV66dhsQICf78XSWnvmCvexRFYWZSBBcr6AuT3QUXPfwxsB3OUI7YdZrscLppn5LaUHY4aZoeUh1BCs4xgEdRyImW44fKDjz7QzV+/tExrH79IDadah/+yQHwt61VYC/h2T4MgaLkIizNVgMAHlqcQaJQziJ4FIX3b56FTXfPxYFHzsfSbDX21HaFXLZBmDiwBWeyStonFoIweWA7nGIfXS1vedQ/1uT36Ti2DmFEEwzMo5TUAkyXs9ti7yP3/nEYiVqgvLy7lsuXnigKnqJk5YDxluHI9pgs3VCUFPTjWVuUhHmeWbcYRd8FqYBHYW6qCnwKnBGdxeEacXHIGq1Ey706nOpep1rC2MJ1OP0wh5qWGA6T3YUuswNzU5VYkBGJ5TnRKBvDPF1/Mdic4FMYtQrj5jnJaDfY0KJnGkJmr422FBVjHGS2u3xGLLH33+E6nKxTbChlra0+Mji9f77F4Q5JTJTe4sQXJYMbWJKCc4zIiwtDl9mBT4+3oLKD6XSuH+KNCRSrw4X9dTrcNDsJ3941FwofuywUReHp1Xn4/OezsbogLmg/mzAxkIsEiFaIwaMo3DArETanGzsqJp78hRAajDYnZEI+1HIRtEYb1h1tDomSghA6hjINyosNw8KMSHx48yyo5SI8tDgDK3KjcfX0eNR3mUM2t+1y07A63aNazAHMLGK3xQmdxQG5iI+4MDE3SxgMnC433j7ARH28s3YG3rh+etBee6xZnqPG+tvm9HGtDSb/vmIqvr6j2KfkWCkT4sbZSfjmZDtKW3qw6Pk9IzakY2NWosP6djgB4lQ7HtjYDqcfUvM5Kb0GPMWeDYrChDC0GWzomGDjOj1WJxRiwaibKAmeAk3j+f26LQ5EeApIdgPr8U2nsfiFPQNURFyXVTK0rFci5CNKLkJzd+juzex9P3aQGU4gNAVvq2Ho3ymggvPQoUO45557cP755yM3Nxfr168f1cGdS/x8bgqevCgXf1yVg8L4cBSnKIM6gN3YzbxWflxYn7mM/vAoCqkBBuMSJh/TE8Ohlouw+WTbeB8KYYxgbrp85MYooDHa8a8dZ/DgF2VjGp9BGB1DSWoVYgH+fUUBcjzjEtMTI/C3S/OQHS2H1ekOSYYiwHS4AEAmGl1+ZoRUiG6LAzqzHSqZEEUpSpQ09wRNWskuoB5bkY2p8eFQDZNfOZGhKArJIezQCvg8Trbri4UZTKG70XP/ePdg44h+Tl2XGWFiARdNA3gVnMQ4qA/767pCdg6zOJzMueYrFqU/ai93ZLZTVpSkBADsq9X5fM54YbAOPzvpD6yrNJu5qTXZufljtuBkVRnr+0XRseMBEX4cR2KEBM360Bkwscc/mEstEJoszuGUNgEVnGazGTk5Ofj9738PiWTwixVhIEqpEBfnx+LSqXF4a+0MzEtTQWdxDLBhHils8TpRZESE8YVHUViWrcauyg5uwUg4u2EMC4S4dmYCpnvC3uu6LChvH/0sFmFsGCyHcyjS2KiJrtAs4Fnp1WhmOAFWUuuAzuyASirEtPgw6CwOfHc6OCoMdpE1UYPpJxOsq/BWj0LG6nTDOQJX4RqtCelRsj6dJ5VMBJVUSDqcXmhNdjz4xQn86quTIf05tgBmOAHg/Ztm4p0bZ3Jf58TIkRghwdYJZhzE5F+O3s2ZnTXWGOygaRodRhv3Pe8NIAoDHWt7bP7PkSZGSNAUwg5na48NYWKBT6UjG7P07cngjvQBGFZRFVDBuXjxYjzyyCNYtWoVeDyixh0NbCRJYxC6nC43jf11zI5TspIUnASG+emRsDndOBUE8wfCxMdgcyJMzDhzvn79dHx9RzEAoGIIowPCxGKoDudgpHkUK3VdvfeSDw834e0DDUE5JjPb4QzKDKcDOosDSqkQhZ5Nkcc3nQ7KNYotOIdS+BD8I8KzeDfamPfe5nTjVHtg1xGaplHTaeY6mt5kqGUki9ML1v001Nfq3hlO/64vU2LDMDWuN2qEoiisnBKNg/U6nGydOLOcBqtz2PxLf5AI+VBKhdAYbTDZXbA43FynVyrk44mVOfjfddOxuiCWu970HgPTPPKn05oYIUG7wRayaKi2HqvPSBSg1wvg6xNtXJxMsGjtsUHqw2GdhVSN40RqELM5n91eja/KGOnLaHehCWcPbCZV6QQc8icEH3aOBWAWBvHhYoRLBKTgnERYHW7weRQEAcR5qKRChEsEeHNfPbaUa+CmafxnVw1e3l2HI43dQz632+zAf3bWDNm9ClaHMy1SCpPdhaoOEyJlImSq5Vg5JRoAcDIIBSdrQuNLRkYIDG9Z4JKubYSXAAAgAElEQVQsRl4bqFlMl9kBvdWJdB8FZ3okcar1ZndNb7cslO6l9gBmOAfj5jnJUMtFeHb7mQnz/hlsw+df+kuMQoSfznTit9+c8nzdez1ZXRCHmUkRiA0To8tk71Mw9s5wDn8cKZFS0ADKA9zEGQyb093nvWgz2Aa9DirEArx4VSEABH3Tp63H6tOoiCU479AwUBSgVJK5QW+mhkkgE/FR1WUJ6G9T1qxHTYcJefFh2FWlRUaUnHOF+tXybPJ3JnAolYwjYHmHiXwuzgE6jHbMTovs817nx4fjTGdg1xhC8ODzeYH97fk8SIQBPgdAmlqO0iY9Ht90GoWpvWYfh1sMuKAwYdDn/XVbKb4qacGCnGisyI/1+Riep3MaGykb1edoeUE8l/8Yp5IiUiXHC2tnofjv21HXbR31Z7TbzmSFJsYEN0rkXEXIp+Bw0ZiZGokqrQkVWnNA79GuOmaz47zs6AHPm5Uehc9LWtFhdyMnNszX00dNwOfeOFLTaUGUnMlHrDfasSA2PCQ/h++Zw1ZHyqEcYoZ3KJQA7luahT99cwo1PXYUeV1vAoWm6aCcqwabE+pwSVDe71S1ApXl7dwGVlpc+IDXTYsJAw3Azucj2qMqtIMCn0chIXr468+lM5Pxjx/OYP2JNizK7zXw7DTZsflEK24sTvH772KxuzDnqa14aFkWHliaBYBRe8zNiBr077EwTwSgDBqLM6jnSEO3FRnRAyMZWcak4KRpoLubyCf6MzMxAj9WdnB/m7cPNGB7pRavXz990BmeRz493kc6BTBzmx/ePAsSIZ/8nQl9WJStxvv767HndHsfaQzh7MLqcKHb4oBK3PcakKqUYOPJdnJdGCeUSllAf3u9yQYxnxfw+6X1knd9vL8eAGMM0tRpGvK1Oj2ugkaTbdDHaXTM910256g+R+E8Jo7B7qKRE9X7d8mOluPTI024oiAWWeqBcV7+QNM0TjR1I0Yhhj6EZhznEg4X0zFRCChMjQ3D0Qadz/efpmn8eKYL0xLCOKOmBp0FT317CjEKEVLDRAOeVxjNLHK3nWhFjJgPi8OFOz4+jksL4nDDrMSgHH+g5954YbQ50dZjxdqiRHx0pBnHa7sw1UdXOBjoPee7zWRDNz1yOecF6Sr8hUdhU0kLMiNGpiiwOly459NSzElR4n5PxudQuGkaq/93ADfNSe7zGaFpGj0WB8RUcOqMBxakYl5KBJ76rhIAIAU94HXDBEwxWNXUDbknjLBVZ4ZSKvT7+nNxXgy+KmtFW4eBW+8/+FkpDjV0I18tQ0aUf9fCHzzztB8fbEBxYjgsDhd6rE6oREPXAzEKESpb9UE7R8x2F2q1Jiz3RC/6gkhqx5HiVMaptqnbAjdN4+XddTitMeL1ffU+H2+0OdGgsyAhQoL7F6bh6dV5uHt+Kv57ZUFAJhOEc4cHl2YhSi7Ck1squMgFwtnHYIYpsWFimOyukMq0CCOj02THneuOo6RZz31vpHmXt87pzWv85FgL8uPCMCVGAe0w8QVOj4PxULNEwZLUUhSFV6+djteum9Yn7mOup0Py2DflI5bo/XimC0ca9Vhd4LtLSxg5MQpG/txusMHqmeet7TRzLpclzT349dcnserV/dBbHDDanLj30xLorU5cWhAHno9OTVy4BCkqKQ41MF3Qb0+2o7LDhOd31WBXdWfI3VonEqyssShZiSi5CFVBnqvzhl0D+GsaNBgSIR+pkVLUjsL46a0DDTjZZsA7Bxux9r0jQ96jLA4X87kw2vHcjjN9/s1kd8FFMy7YwSAhQoLLCuLwyyUZAJjPf3/Y+6zG6/ra7TFD85f56ZGwu2ic//weTq5+spUZLWgLIFf5h0pm/jdKLsKN7x/FHetKAGDQGU6WFJU0qEkZVR1G0ADnou4LUnCOI0uz1eBRwH931fSZtfn8eKvPk+9Iox5uGnhiZQ5+NjcFF+RE447zUpFEjIIIgxAuFeJ3K7JR22nGlvLgu5IRJgbsja9/kHt/m3fCxOHpbVU43tzDOYECzBzQSOz9r5yegL0PLwTPs7ZfnqNGtEKEDuPQ1vdswcnOH/nCZGf+bbQ5nABQmBCOWZ5oBZZbi5Px2+VZqO0y40D9yOIW9tV1QS7iY21R0vAPJgSEWiFGokd+2dJjxXflGlz7zmHc+2kp7E43tnk6LG4a+LK0FZvLNdAY7Xjp6kLcuyBt0NedmRSB0pYeuGka60tbkaWWQybi49dfn8TDX54Yi19tQsC69WZEyZClluFMR+gKzt4ZztHLWNMj5agZxQzgD5VazEqKwOqpsajqMGHDib4Rbk6Xm3M9/f3Gcjy64RT3b3VdzIaHy01D67nGRcmDU3CyrC1KwsFHzvfZzGHvs94xIDqLA0qZ/8cwMymC+//ndp6Bm6Y5g7Zmvf8OtqwL/el+86DDxSplRStwWmNE3SjdzY02JwxWJ/fzc2MG78wGVHCaTCaUl5ejvLwcbrcbLS0tKC8vR0tLy6gO+FwlPlyCC3KisbO6E/d9VgaxgIdXr50Gs8OFTacGFgfHm/UQ8ikUxodG3084O1mQHonECAm2VQQvZJ0wsRiqwwn03YkljB8Olxuv7qnDziotdlYzRiEGr83FHquTcwgNFCGfh/dunIXLCmKxemoc1ApxUApOvYXNlwvugs6bS6fGgUcBx5tHZnB2qs2AvLgw8HlkdjPYRMtFSFQyBWdztxXvHmIyOWu7zHhpdy22VnRgSVYU5qQo8c3JdjTqLJAIeJiTohzqZTEtPhw9Vic2nWpHVYcJawrj8MzqfABAVYcJTd3nhjS6WW8Fn2LWg1lqBWo6Tdx5ORg0TePN/fUBd6jsTjd4FIJynmSoZWjRW7mutz+43DTcNI3WHisadBYszorCE6tyMSMxHF+UtIKmadA0jbcPNOD6d4/gstcPYt3RZvxU09Xnda55+zBWvbofHx1pQqfZU3CGIHd3sDlKhViAjCgZvj+t4VQZOrMdkQF0OGUiPu5bmIacaDlOtBpwqL636dTsZ2SK1eFCc7cV4RIB+n9ipgzRaQQYVYxUyMeft1SOKqv7to+PY8XLe7HxZDtSVdIhY6kCKjhPnDiByy+/HJdffjmsViteeOEFXH755Xj++edHfLDnOo+tyMbP5yYDAFblxaAoWYlMtQzbPLveeosDX5a2wummUdbSgykxilHLIQjnFhRFYXluNA416NBtCU7uK2FioTEwN93ofvIfNiKiPQCJDiF0vHOwEW/ub8BvNpyCkE8hPVLWZ3HRY3WMKsA8N1aBx1fmQikTIkYhgtnh4jqUvmCVNPoh8qB1FgfkIn5I7ztiAQ/x4ZIRSbzsTjeqOkzID5H5zLkK66QfLhFwHc59dTpUdZjwyNJMrJ4ai4+ONKPL7MDVMxIwMykCjToLqrUmJColw5qeTPPE4jy5hZmVW5atxuwUJTbcycQ5fX68NVS/2oRCY7AhWiEGn0chO1oOu4seNi6v0+zAq3vqfTYmhsLmpCHi84Ji1JMRJQMNoL7L/3P23zvP4MKX9+Gln2oB9MrpL8mPRYPOgkqNCZtOafDy7jqY7C4oxAL8q5+E9tVrp+GS/BgAwN46HdfhVPuQvoaSG2YlorLDhBLPJpnO4oAqgA4nAPx8bgr+uCoXAPBlWe/nvdnPOdC6LjNoMOcOS3GKEv+9smDY91itEONXSzNR1tozoLvsLxaHC7WdZrho4LTGiBuKEof8uQHd2ebOnYuKiooRHRjBNwqxAPcuSMO8NBWmxjEX4OU50fjf3np8f1qDn2q6sKVcgzaDDac1Rlw1PX6cj5gwGVmeo8a7Bxuxq1qLNYXkM3S20aK3IlImHCD/iZaLQIF0OCcKW8o14FFMDtsD56djT20X9tbqUNKsR7XWhNYeG7cIGy3sAmxfrQ6ZarnPeAp2Dm+oDme3xRG0+aihSFFJsbWiA+0GG26anYQ5KUqfweXePLfjDL4qYzZk8+OG3tEnBMbr109Ha48NFEVBKRVCJuTjy1JmUbwoMxJrCuLgcNMw2pwoTlHCZHOCBnCooRuLvWZ0ByMlUorZyRGIDZdg1ZRobnMsPlyCNQVx+PhoEy4dhZHUZKHdYON+d/Z3rdaafJ6vLF2e87ZlCOnl8SY9YsPFXEzF96c1+PBIU7AOG3Ge120z2JAbO/y553C58emxFtAAvjvdgbRIKZfRuiRLjae3VWFbZQfKWnuQqZbho1uKsK9Oh4fXM/Lqi/JiIBPxUZSsRFGyEiIBD1srOtCRHgkgNB3OobhwSgz+ueMMtlZ0ID8uDEabK+CCEwAy1XJIhTxuFnN2coTfG2+spPm6WYmYlRyBSJkooPvHRXkx+PhIMz483IQ1hb7nrYfiuJf/wFXT47GmIG6IR5MZzgkBRVGYlaSE2LODfM2MBBQmhOP3357GlnINAOCt/Q2wOd2YlxacxQjh3CI3RoHECAk+OdaCLvPQMjvC5KO2y4zUyIELFAGfhyi5qM+sCWF8oGkaGoMN189KxPrbi7EsJxqJEVJoTXbc/3kZnt5WDaebRniQirt0z+fhdxvLce07h6Hrd9673DSneBiu4AzEDGOkpHg6aqUtPXh0wyl8eHj4xfHHR5thcTBzafnEhTuoqGQi7m9KURRSI6VwumlESARICGdi3Z66eAr+fQXTTfF21WQluEPBoyi8cu10/GlVLualRfb5twcXpUPE5+Ejr89ARbsRd31SgsMNQ2fLTjY0RjsnQ0yLkoFPAdUdQ+cz6szMedva47vgXF/Sgjs/KcEznhiibrMDv//2dBCPmtnMBACtyb97y6GGbtAA7p6fCpVUiAfOz+C6YUqZEHNSVNhW2YH6LgvyYsPAoygUpygRKRPitnkp+PPFU/Db5dnc6xXGh8Noc+Gz4y0Q8qlRKUNGgkzEx/z0SGyv0nJrqpFcJ/k8iksQiAsToyhZidpOM7rNw6vR6rrM4PMopKmkuCgvNuDNSoqicPOcJNTrLFhfEriiYPeZLogFPPz0iwX47fLsYfOjScE5AYmQCvHatdPw4PnpWFMQh/W3zcH9C9Pwj8vycV6/CzOB4A8UReEXi9JR32XG1W8dxu++OcUN5BMmNzRNo67LzBUY/ZkaF4YD9Tq4J0hI97mKye6C1elGtJexU5JnYe7tIB0RpIXTlNgwXDK117X16zJGNtVlZsw2Oow2sKM7PUNIavUWB5RjUHAKeH2XI439Zvhe21OHH890Dvr8wYLOCcGhKJmZyUxRyXzK5pK8TEoSR5jxyBIhFeKygjhsKtegQsMUX3/dWoljTXq84JFjng3QNM10OD3XBLGAhxSVDJX9jIP6u/ayc4veHU6b080VKT+eYWYem7ot2FmlxYpX9gX92CPlIvAoDDsnzsKa01w9IwFb7p2HxVl9u+AX5KjR1G2F1mTnNp+EfB423zMP98xPHfB6S7PVyI1RoEVvhZsefN4ylCzPUUNrsnPz+MoRdllXezqDLprG3FQVaACHG4ffWGnutiI+XDxsoTcUK3KjMTs5Am8daAjoeW6axvYqLc5LU/mdkkEKzgmKgM/DLcXJ+MPKHCSrpPjZ3BQsHSLfhkAYjmU50Xh77UxMTwzHTzVduOfTUlgCGPgnTEy6LQ70WJ1IjfTtSrc8NxodRjtKmnuGNaPwRaPOgtf21KFFbwVNM6YPpHgdiJum8cY+Zq7qfY+xijfswoztDAC+u3LB3Kn/48ocbL9/PtRyERp0FhhtTqx8ZT+e/7EGJzwW/PHhYuiH6XAqpaHvHlw/KwGXTo3F5nvmYX66qs+iu91gwxv7G7DxZO/MWv/Z1PFYcJ5LzPYUnE637wgdAY/CbXOTcV6aCvPTR78xfuf8VERIBHh1Tx2A3qiIU20GnAlhdMhYorc6YXO6EesVYZEfH4Yyj3svAHx6rAWX/O9AnySDLk9h2WG0w+7ZrPrHD1VY8co+dBhtaPBk57YZbHj+xxoAjHngM6vz8PDijKAcu4BHIVImQke/cQ2Lw8VFKXnTabJDyKcQIRH4lG4uyVaDNc9N9dq84FGUz3NbIRbg6dV5ADAq05vRsDAjCmIBD+uONgMAokYgqQUYaSvj1p2NvLgwyEV8vxy7m/XWUW/uUBSFBRlR6DDaA/L4eG7HGWhNdqzIjfb7OWPbgyYQCONKTowC/76iAEebunH3J6V48cda/OaCrPE+LIKftOitKG3pwaq8GO57dR7ThrRBOpznZ0ZCxKdw1yclSFJK8NnP50AQgEvhuqPN+PR4C97Y34B5aSrOaObttTNxpLEbB+t1WFMYj4RR3vgmO58fb8Vre3szlM/PiMIMZe97wi7MvM0tfC0WwoPoBktRFMIkAiQpJWjWW7nZoHVHm4FZTEdldrISP57pxIayNizKiuK6mdVaE9p6rGM2wxkXLuEMNPJiw7C/TgerwwWJkI/tVcx8E9vpcdM0/ruLWUjLhHz8YWVOyI/vXKcoOQLz01W487yB3SaWexemB+3nKaVCLMqMwrbKDjhdbnRbHFiWrcb2Ki0qNEZkngWznZy7uNc1oThFiW9PtqNCY0SWWo7/7GJMc747reG6zOwMJw2mqEwIF2PDCWYz5p/bz6BFb4VKKoTO4kBjtxUX58fg10uzEBZk2Wn/6KXN5e14ckslKADrb5/DzY8CTMEZJRMNujGklDKy2v31OqSoBp9f9SZJKcUtc5JHNDsZDGQiPuakKLHb46LrLSsPBIqi8MD5vefO7GQlDvohHW/WW/sYBo0Udl64ttPcJ65lMLQmOz451oLLCmKxPICCk3Q4CYRzkFlJSlw3MwGfHm/ps3M60ajQGHHFmwfxZWnriEPhzyae+q4Cj286jZJmPfbUdHFyWmDwglMuEiA3humkNXVbsaPKv3icui4zKtqNqNaaIOJTuHl2EvbX6XCi1YATrQaUNOvx0PoTeOtAI97aH5gcZyJisjvx6IZTuOjV/bjktf1cGPdwVHeYsOaNg/jXjuo+32fzCVm4DqeXpNZ78ZXm6VCHD2OUMxISI/oWnG4aONqoR16sAlNiFdBbnXjq+0q8+GOvXPH2j47jl1+ehMXhHhNJrTcF8WHMMTYxphQ/eFzbT7YZsPKVfThU340vSxmJ8KvXTQtol50wMiRCPv57ZSEKxjCWbVoCM6dX0tIDGsCMpAgI+RSqPd3vdoMNJ1tHFqUzEdD4iLMq9szh3fLBMXxzog0OFw0Bj8Ku6k7uHujtw9Cit+CI5zxJVUmxvUoLFw0szOjtMl9RGB/0YhNgrmX76nRo6ragx+rA37dWQcij4HTTONak7/NYrcmOKPnQktOrZyQgSy0fNkPSmwcXpeOm2eOXv8u6LctF/KD9jYtTVWjRW4eMBjLanOi2OEbd4QSATE/ByWbCDsdBT/f1mhkJARkNkYKTQDhHuf/8dCQrJfjT5gpsrejgOlfjTbPegofWl6Gm04R3DjSgqduKv22twnM7a8b70MYdo42RKt2xrgQPf3kCB+p1qOsyQyzgIS588Bm2W+YwN2QeBTy5pcIv440715Xgpg+O4miTHqsL4vDgor7dizvWlUDAozA7RYmd1Vo4Xb6ldpOFzac02FGlhdZkh8Zox87q4QvzbrMDj3x1gpsj8qb/vCHb4ewfXfPJz4rw7yumch3iUGRJJkZIoTHYUO0lRTytMWJZTjS3YAIA2ivNzewltx/rgnNOigpyER8/VDKutSUtPVCImTmhLrMDG73iIFICWJwSJheFns8mu0kWoxAhPVLGfY4f+LwUP/voOMpaerg5aKeb5uY+JzpshzPGq+BUy0X47XJGdfR3j+nP1TMS0GV2cOdkl9mBSE9Xr6XHhmNNevAo4J9rpnKvc0FONMIlAlyQo8a0xNBsErAF1qMbTmHDiXZYHG68fv10iAU8lLf3fQ86TQ6ohyk4F2dF4eNbizgDzckAe/0cybjKYJznMQf95FjLgPldlmbP/K4/Bl3DERsmhlzER1WHfwXnoYZuREgEyBkm67M/k+ddJRAIQUUq5OMvl+TB7nLjsY3luPG9I1xMwnjgdLnx6p46XP7GIeyt1eG6d45gW6UWN89OwjUzErDuaDMe/LwM2nE8xvGmw2SHgEdhicdw4UB9Nyo7TEhVSYfcaVySrca+hxdi093zEBsmxv2fl3KzUb5gd09ZcmIUoCgKV05jInUy1cyO6JrCONxYlAi91YmvyobP8rI4XBO2MK3rMkMu4uM3yzIBDMyXe+HHWhyoZ2SeZjvz360fHu3jAFwQz3SSxQIeTrcb+zjD1nWZESERQNrPYCEjSo6FGVF4YmUu7piXgqnxwXdbTVRKQAN49yAzW5oQLoZSKsRlBbHIiu5dNFDo/Qyxi8MIiaBPt2QsEAt4WJwVhW9OtOO+z0rBo8B99gBgq6fjueOB+ZCLyGTQ2UqqSgq5iI99dUxHRSUTIitazhWc7DjBbR8fxy0fHIXN6cbLP9XipvePoqRp4ip3WDRGG/ieWUhvrpqegJs9XTsKQG4MI9XsMjm45+XFhoHPo9Cit6KspQdZajnSomT44KZZuOu8VMxNU2Hrfefh6dX5Acdd+MuNRYmgAFR1mLC9sgOZahmmxIZhSowCp9oMfR7b6UeHczLCzuFfXjh0JEggJKukmJuqxLqjzbj3s1Kfj6nzRKIEY8ONoijMTVVha0WHX74eFRojCuLDA/5ckYKTQDiHyY8Lwxe3zcFfLp6Clh6b33LLUPDhkWa86ZFmxni6QDEKEW6bl4KHFmfg4vwY7K/X4ZltVeN2jOOJ3uJAp8mO+xam4dk1U5GslOCDw0043NCNJOXwNx02IuVvl+ZBKRXizf0NqPXctPrDdkB/uSQDq/JiuFy931yQhe/unYd/X1GAywpiccucZCxIj0RxihIv/lQLq9fNqr+xUI/VgZWv7MNjQbbnDxb1OgtSVFJcOzMRF+ZG47TGiB6rg5Mtv3eoEQ98XoYb3z+KZS/txcdHm9DSY8MfLszmdqSfungKVk6JxtOr80AD2O+RPb97sBHfntIMWbhFyUW4e0FaSBaHs5OVKE5h5r8WpEfi89vm4POfz4ZcJICA1zs/xLpfOt00usx2XDMjAZvuntdHBjxWXDMjATSABp0Fz6zOxyzP/BrAmIREyoTD5nQSJjcURSEnRsFJwSNlImSp5ZzBibdaoKbTjOPNenxe0gIAeHtvXciOK1imae0GG6LlIp+qhnsWpOG2eSl4bEU2V5B2me1wuNyo77IgK1qOuDAxGnUWnGwzcN3g3FgF7pyfCgGPClmhyZIdrcAr104DAJS1GrhuX15cGCo0Rq7r53S5obMM3+GcjEiFfHx/7zw8vCQzqK/74CLG3KlBZ/EZkVLTZQafAlL9nHcdjrVFieixOrGtosPnv7PGTE43cz/MGCIndjBIwUkgnOMoxAJcOCUa8eFiv5zRQsWemk7kxSrw4c2z8MVtc7DhzmK8tXYmFGIBxAIenrxoCn5WnIyd1Z1DxjicrbDFIWtM4G2aERNAJERujALrbi2CiE/hq7K+2VsVGiN+PNOJjSfbESER4JoZCXjq4inczjTrTBgfLsHjK3MRJWdMIG4tTobJ7sJeTydiW0UHlr6wl8sRBoBX99TD4nBjR5UWL/xYi1f21OH1ffV+5Y2NBQ2eghMApsQq0G6w4YKX9uG+z0q5SBH2cS43jU2nNJiZFIE1hfF45rJ8rLu1CElKKf5ySR7mpUVCyKdQ2qxHa48NL3qiHAIxWAgmMWFivHTNNHxzZzGeWJUDIZ/Xxwjo1uJkzEtVce6XnSY73DSQpZZBNE7ytoL4cFw5LR6PLM3Ekmz1AAdI0SiiAAiTh1wv2V6UTISsaOa6V9FuhNZox6q8GHx0yywAwOZTjKwzQiLAD6c1nINrMPnPzhpc/86RoLy2xmAb9NotEvBw74I0XD4tnpPPdpkdqO+ywOmmkaWWIyFCgu1VWpjsLpyfGeXzdUKNtyS/0DPfmx+ngM3pRq1nJpBVJUXJx8fcJ9SoZKKAjPj8ITdGgdeuY4v5gXPKNVoTkpTSoF2fpyWEI0ou8rkG/K5cgwX/3Y0Xf6rF37dWwuGikaEOvOAk24MEAgEURaE4VYVtFR3osTqC6pTpzRmtCY9uOIVrZyTgulmJ3PdNdidKWw24aXYSNxcQ7yPbaU6KEu8cbMSJVkNQrPcnE016ZpefLYr+74IsXD0jAU4XHbAMUyUTISdGMWBm47GN5Vw34fZ5KRD6uaiflayEUirENyfasCgjEk9vq4LZ4cL6khasyotBt9mBDSfasDAjEqfaDPjgMCPtdNPA//bWQybkY1FWFH6/ItvvTK9gYne60aq34pJ8xv33imnxkAr56DLb8fq+Bhxu1A94ToPOgutmMp9hqZDfZwNAwKOQpJSivtOEmk7mxsx2g8eTuPDB530i5ULOgIpzzwwbX+fh363oDXqfEhuGf10+FSlKKa555zAEfBKDci7AykkBQCHmI9tznu2u7QINxtU1O1qBSJkQ2yoZhc6Ns5Pw8u46lLX2oChZCafLjX11OsxNVY1ogd5usKGu04wznSZ8eKQJAPBFaSvCxHykRcpGbKTUbrBhSuzw127vDic7q5oVLec2AlflxYzbtUXI5+E/VxTgb1srOcOjfM/vdKrNgOxoBU555jmzowOb+TvXyffIpktbegZsKNR0moPq1ExRFIpTlNhXp8Pdn5SgWmvCpVNjcUFONNaXtsLlprmRDABIH4EjLyk4CQQCAODq6fHYeKINz+2swZ888QTBolprQlKEBE9uqUCDzoJ/7jiDC3LUUHukeruqO+Fy05w0cTCmxoeBRwEnWnu4gtPpcqOp24q0EUg8JhPN3VbwKHDmQGqFmPv7jYQUlRRHvAopg9WJBp0FSqkQV0yLw41F/jv/CXgUbpqdhBd/qsXTP1RDb3UiJ1qO4809aNFbsbNaC5vTjfsXpnMdCgB45MsT+KmmC5FyIbaUa5CqkuKOIWIXQkVjt9VAIgsAAB+XSURBVAU0wLkjKsQCXD0jAQCwrVKL2k4zHl+Zg799XwmXl5ruwiE6lqkqKWq1ZtRomSLu1uKkCZ0VGSkToc1gwzPbqjj5akzYxJLALfIsuv5+aR5n5U84u1mSpUbjPCtSVVJQFIUouQhKqZAz5WLNtnJjFNhXpwMFZrb8tb312FurQ1GyEr/ZcAq7a7pwzYwEPOpnDJjJ7kS7wQYhj4ebPzgKkydbclFmFJq6LXhuBxNXwudReHftTOTGBlZMOV1utBlsfuWrcx1OkwMtehsEPAppKikzq5mqxEV5sQH97GCzICMS3949j/s62TN7+5fvq5CklKKspQdCPtWnW00YHomQj/zYMLxzsBH1OgueWJkDhVgAu9ONpm5L0BUzC9Ijsblcg6NNeoSJBfjoSDM+OtIMAY9CikqKu+en4kSrAZ8dbyGSWgKBMHKmxIbh1uJkfHuyHRtODG8AMxg0TePN/fXYW8tkU31/WoMb3j2C85/fg/J2I66bySzkT3s5CX50pBnpUTLMGiYDSi4SYEpsGD483IxHN5yC1mjD2veP4pp3DqNyDJ0JtUYbntxSgS6zHSXNejy+6fSg85DBoklvRWyY2O+u43CkqKRoN9g4E5zbPj4GAHjmsjzctzA9YIv3G2cnIT8uDF+XtSFMLMDfLs2DRMjDn7ZU4MPDTciOlvcpNgHg0QuycPu8FHx8SxHOS1Phs+MtIZHBDUe9p7OX7iNa5h+r83FrcTIuyY/FVK9OxrxUFZRD5L+lqKSo7jDihZ9qIeJTIVMNBAvWBfbzklaUtvSAz6OQ7Mds8HiwPDf6rMhhJAyPQizAvQvScHE+U1RRFLP4bfG4dLIFJ3vvoMFsnizMUmPjyTY0dVu4nMTPjrf4Ff2gNdpw43tHcd07R3Ddu4dhsrtweWEcfrs8C/9ck4/Xrp2OG2Yl4s8X5yJcLMDLe2qHfc3+1HVZ4HDRfnX9BHweIiQCdJrtOKM1IT1KBgGfh2SVFJdOjQuJs/Vo4FEUHlyUDrmIjyc2ncaBeh2mxISNmzx/MlOcymz+7ajS4iXPaEa9zgw33RtnEixWTIlGplqGMLEA3907Dxvvmosrp8XD6abxi0XpuHBKDB5ZmoldDy4YYH7nD+TdJxAIHLfPS8XMpAg89V0lDjWMbJ7zy9JWvLqnHg+tPwGz3YV/eXaCpyWE4/Z5KbhnQRoAcNb1zXoLKjRGXF4Y51cH6G+XTkFBfBh2VGlx0WsHuEKPLXDHgh8qtdh4sh13rivB/Z+XYUu5Bnd/UtLHNCfYNHdbg5K5xcKGazd2W7Cvrgt1XRbkxSowbYTyMAGPwpMX5WJpthovXl2I1EgZfrs8G6XNemiMdp9ZiXHhEtyzIA0SIR83FiWhy+zAd6c1Pl49tNR2sY5/A2/gaVEyPHB+Ovg8CuelqcDnUfjsZ7Px3BVTBzzWG+/Q8xmJw4dpjzcqr5nOr0pbkRMtHxd5M4EwHPEelQef6s217d/tuX1BGrrMDvziizIAwEtXF0Is4OGZbdX4144zePtAA2eEwsLmXH5wuBnNeiuSlRJmXi1Kht9fmIOrpieAoigoZUI8sjQTF+XFYnVBLPbW6vxyTz/UoMPmcibSh73/+dv1i5SJoDM7UNVhnBSbLVdNT8Cza/KhMdpR1WHC7JSJfw2ciMxJ6TVL21rRAZqmOdVMxghkrUPBoyh8cNMsfHXHHAj5PMSGifG7FdnYdPdcLM7q7cSPdOOAFJwEAoFDJODhxasKESkT4v1DTQE/f1tFB5cdBgB3fVKCLrMDr1wzDW/eMAP3LEiDQixAslKCCg2z03yonnFEPS/NvxmUxAgpXrpmGmZ6ssVuLEpCllqOg8NkS55uN+D1ffU43W4Y8nH+UOMpcht0Fticbjx6QRZ0Fge+PdUOmqbx45lOnNH6l2nlL816CxIjgtdxYmdBz2jNOFjfDbmIj7dumAHBKDqoaZEy/OOyfM4q/uL8WHx4SxH+cVk+bvCa2fVFcaoSWWo53j3YyM0pjRV1XRbEhokhEw1dYN08Jxnv3jgTaVGyYTvN89JUmJYUgf9cUYAnL54SzMMNCZcVxOFvl+YBAKxOdx8zEAJhIsHOIseGSzizliSlFJdMjcVjnrnf8zKi8MslGWjpsSFSJsTsFCVumJWIo016rDvajJd31+GTY83ca55qM2DZS3vx/K4afFXWigtzo/HeTbNQlByB+89PH3gQHthC96JX9+OV3bUobRlo8MJy32dleGJTBbQmOyo0RogFPL9jLaIVIlR1GKEx2rk51olOkZez9PKc8TFMm+wUJSvx5g0z8LsV2dB7xl5qOk3gU6HJIBbweQPUOMFyKScznAQCoQ8iAQ9XTY/H6/sa0G6wIdZPB1SapvHOwUakR8rw4S2zcP/nZTjWpEdhfDiKkvvubk6ND8f+Oh10ZjvWl7YiRiFCWmRgF8+nLslDtdaE+Wkq/GcXjc+Pt8DqcPnsytA0jSc2VaC2y4w39zfg2hkJON6sR26MAo9ekBWQTPXpbVVYX9qK7Gg5Z7pz9fR4bDzZjo+ONENjsOGtA41Ij5Lh05/NDuh3GoweqwNdZgc3YxgMMtVyRMqE2Fmtxak2A4qSlaMqNof6Of7syFMeGdZD60/gvUONuHMMZznru8w+5bT9EQt4fnckkpRSfHH3eejuDq3UOlgI+Dwsz1HjMc/XY529SSD4C9vhTAjve2/q7z2wtigJc1KUcLho8CgK9y1MQ0F8ONIipXhu5xm8sa8BlxfGQybi471DjbDYXXj/cBPEAh7ump8KhViAV6+dPuSxTIlR4ImVOfjr95V460Aj3jrQiIRwMX67IrvPJqq3lPcP35ajvM2IGYnhfsthU1RSblM1M3pyFJw8isJd56XiQL0O2ZPkmCci0xLCIfdshpa19qBaaw6qQ+1YMbmOlkAgjAkXTmHcOrf7kcvZ2mOFm6ZxtEmPCo0Ra4sSIeTz8JeLp+AXi9Lx4tWFA6SyS7PV6LY48OAXJ1DZYcJDizMCNlSJDRNjQXok57Brd9Eoafa9u3ygXofaLjN+tTQT52dE4uOjzShvN+KrsraAJJxntCZ8UcJEiaRHyvDc5VPxv+umg6Io3FiUiAadBW8dYJzcajvNuPG9I6OOcLE53dhZxRhk5MQE76Yt4FFYmq3GD5VatPbYfEpex5r56ZFYnBmFT442h1Se7A2bs5ka4IbH2QhFUXju8ql46epCzPNTcUAgjDVshzPBjxGD7GgFp7igKAqLs6KQGinDbXNTYLA58dreOugtDuys0uKGoiQ8c1k+/nFZPlL92IBiX3N1QRzevnEmHl6cgbvOS4WAz8Pj357mJLvtBhue/aEaAh7FdFkb9aAo4JGl/mc3pngdT16ABkXjyZ3zU/HGDTMmtGHaZCA9ipmt3F+nw8F6XZ/u8WSBdDgJBMIA0iJlyI6WY0eVdkgpZFWHEWvfO4r56SpYHW6opEKsymOK1ZgwMW6ek+zzefPTVJAJ+ajQGLEwI5IrcEfKzMQICHgU9tZ1Ya4Pp9vN5RqESwS4ano8rpuZAK3JjjCxAGveOIgnt1SiqduKS6fGorSlB1srOnDznCTMShp4QWeL0zUFcbi+KBFZXp27ZdlqXD09HjSYWI2b3j+Kyg4T1pe04mdzU0b8u73wYw0+OcaEmecE2Vb++pmJ2HxKgwipAMtzhndLHAvWzk7ErjOd2FbZgUunxoX852mMdlgcbqT5ucA82xmvPD8CwV+4DucoZtqnJYTjsoJYzokTAM7PjPR53feHvNgw5HniQJJVUjy+6TTuXHccd81PxW+/KYfJ7sK9C9Jw27wU3DYvBUI+BbnI/yW4t3ySjUkhnDvwKApFyRH47nQHAEyIDeJAIQUngUDwyXlpKnx0pBlmu6vPbJvR5sRnx1twUV4Md6PeW8sYDP1ueZZfRiMSIR+3z0vBCz/VYknW6Be4MhEfS7KiOAvvu+anQeyRm9idbuyq7sSybDUnnWVnErKj5ThQ34039zfgzf0N3OtVd5hw1fR4XD8rsc/v06JnjHv+sDJnwDEI+Dz83/Le3MCNd83FnzafxjsHG5EXF4biFOWIdnm9o0vY3LVgkRYlw+Z75sHudIdETjsSZiZGID5cjG0V2jEpOOs887ik4CQQJgcpSikuzo/B4syRb5JRFIU/XJiD3BgFnt3OGNsVjtAwrT+ss2hZqwEPfnECEgEP/75iKpeVqZQG7lidMkEdowljx5wUFXZWd0LEpzBzGEf/iQgpOAkEgk+KU1V471ATjjXpscAzz0XTNB5efwIlLT3YX6dDaUsPrpwWj/npKsSEibkdXn+4eU4SpsaHBc3B81fLslDXZcF7h5pAURQe8Bg97K/XwWR3+cysuml2Esx2N34+NxmHG7tR3mZAaqQMX5W14aXddShvN+KZy/K5x2sMNsT4OdMaGybGH1fl4oHPy/DA52WQi/j4+o5iRAS42GAlubcW++4WjxaZiD+sWc5YQlEULsiJxsdHm7G9SotlfuTUjYa6LrbgJAs6AmEyIODz8ORFozfioigK185kRiH4PCpokVORMhFWTomGxmCDxeHGw0syRi2BTIiQcMZHhHOTJVlR2HCiDb9bnjXhonD8gRScBALBJ9MTwiER8PBTTSdXcB5t0qOkpQciPoWjTUzn7abZSSMys6EoKqhzCGq5CB/fWoSnvqvA+4casTgzCoUJ4fihsgPhEgGKUwb+rHlpkdysGislrOk0YUeVFiqZEHtqu2BzurluabvBhmkBFMhx4RLcNT8Vv//2NEx2Fyo0RhSnDpT8+uJfO86gudsCjdGOhxZn4KbZSX7/3MnOLXOScLxZj99vLMcvl2TgsoK4oEd00DSND48047+7aiAX8YPePSYQCJODXy/LCvpr/uWSvKC+Hp9H4ZVrpgX1NQmTi5gwMT64edZ4H8aImRgaKgKBMOGQCPlYmBGJHVVauNw0ajvN+L8NpxApE+KL2+ZgbVEiHluRHVTn1GDwyyWZiFGI8cDnZTjS2I0dVVoszVL7LRnNiJJj2/3z8dDiDNicbpQ0M4W1m6ahMdoRE6BF+LKcaNw+j5nhZONUWNw0jaZuCwDg67JW3PLBUby2pw4/nenEuqPN+MkTWD4j8dyKqFDJRHh2zVRESIV4dvsZ3P1pKZz9MvNGy1++r8R/d9WgKDkCj16QRUwtCAQCgUAIEaTDSSAQBmVFbjS2VWrxRUkrjjfrYXe58cHaIsSFS/DLJf477I0lCrEAr18/HVe9dQi//aYcFocb18xMCPh1ZiUpIeRT2FGlRXGqCl1mB5xu2u+YGBYBj8Ld81Px+fEW/GvHGaSopJjvmeV5+0ADXt1Tj/npKm4OtrHbgvlpkVBKhVg9NRYF8WEoCNJs0WRCLRdh/W1z8MkxJjPvVJshaNmQRpsT355sx+WFcXhsRTYpNgkEAoFACCGkw0kgEAZlcZYa0xPC8ez2amyt6MBlBXEhCRsONnHhEkxPjEC3xYHZKUq/sxO9kYn4WDklBhtPtqOtx4p2gw0AAi44AUY+bLQ5AQAPrT+BZ7ZV4e0DDVh3tAVRchH21uowNS4Mf7gwG0abC99XdGBuqhK/WJyBZedwYDb7HgDA7R8fx5+2VMBNj77TebRJDxcNrJwSQ4pNAoFAIBBCDOlwEgiEQeHzKPz7igLsqWWknZMpDH5uqgqHGrqxdhQmC7fMScYPlR24/ePjmBrPhHSPNMD6oSWZ+LqsFS43je9Od8DgKUDfuH46+DwKSRFSdHtldvo763m2E+8V7v7tyXbsPtOJa2Yk4KL82BFvfhys10Es4AWtY0ogEAgEAmFwSMFJIBCGJEwi4LI1JxNXTY9HTJhoVEVyepQMz11egHs/K4WmSou75qeOOPvthlmJnMMgTdPYXqVFslKKHK/ua4RUgNwYBaIVIlw4CXO2QgFFUbhyWjzK2w24rCAOX5a24o39DfjwSBNeu256QM7ILAfruzEzKQIiARH5EAgEAoEQaiiaDoI+aRjcbhqdncZQ/xgCgdAPpVKG7m7z8A8kDApN07jn01LYnG68cf30CZNXea5C0zSa9Vbc/UkJpEI+Xri6EPHhAzcB3DSNBp0FqSppH9lsu8GGS/93YEycf8n5RyCMD+TcIxDGh+ho35vAZOVEIBAIQ0BRFF64qhBv3DCDFJsTAIqikKSU4s8XT4HWZMdN7x/FrurOPo9xutz41Vcncc3bh3HHuhJsr9Jy/3aksRsAMMdHTA6BQCAQCITgQyS1BAKBMAxEejnxKEpW4v2bZuGxjeX49dcncWFuNNQKEZKUUmyt6MCxJj1yYxSo1Bjx+LflSL+5COlRMpS29EAu4iNLPbJZXAKBQCAQCIFBCk4CgUAgTEqSVVK8ecMMPP9jDTaXa2B1uGB30eBTwHUzE/DrZVnQmuy4/p3DeHJLBV67bjrKWnowNS4MfB5xpyUQCAQCYSwgM5wEwlkMmWMhnEt0WxzYVtGBVXkxUIh791O3VnTgsY3lSIyQoFlvxW3zUnDvgrSQHw85/wiE8YGcewTC+DDYDCfpcBIIBALhrEApFeLqGQkDvr8iNxpOtxtPbKoAAFw0ZfK5LhMIBAKBMFkhBSeBQCAQznouyotFh8GOuHAx0qJk4304BAKBQCCcM5CCk0AgEAjnBLcUJ4/3IRAIBAKBcM5BrBcJBAKBQCAQCAQCgRASSMFJIBAIBAKBQCAQCISQQApOAoFAIBAIBAKBQCCEBFJwEggEAoFAIBAIBAIhJJCCk0AgEAgEAoFAIBAIIYEUnAQCgUAgEAgEAoFACAmk4CQQCAQCgUAgEAgEQkggBSeBQCAQCAQCgUAgEEICKTgJBAKBQCAQCAQCgRASSMFJIBAIBAKBQCAQCISQQApOAoFAIBAIBAKBQCCEBFJwEggEAoFAIBAIBAIhJJCCk0AgEAgEAoFAIBAIIYGiaZoe74MgEAgEAoFAIBAIBMLZB+lwEggEAoFAIBAIBAIhJJCCk0AgEAgEAoFAIBAIIYEUnAQCgUAgEAgEAoFACAmk4CQQCAQCgUAgEAgEQkggBSeBQCAQCAQCgUAgEEICKTgJBAKBQCAQCAQCgRASSMFJIBAIBAKBQCAQCISQ4FfBeejQIdxzz/+3d/8xVdV/HMefIFyK+aOuEuiVf9DuCXEGjAQErZlry42ytFE5Hfde5iybDG1Fc6n1BwEzS6+ViTMsGer8EW1Gq/5wWYFbzSRNLFCGjiB+qnFNCM73j+bd7tS+F7kXQ1+Pf9g553Pe5/P54733fXPOPXc5s2fPxjAMDhw44HO8vb2dgoICMjMzefDBB3G5XDQ2NvqM2bNnD0uWLCElJQXDMDh//vw11zl58iQOh4OUlBRSU1N5/fXX6enpufnViYxwgci9q0zTxOVyYRgGX3zxxXXHXLlyhSeeeALDMPj5558DvRyRESVQ+VdbW4vD4SApKYmkpCSeffZZOjs7vcdV+0R8BSL3mpqaWLFiBWlpaSQnJ5OXl0d7e/t1r6faJxJcfjWcHo8Hu93OmjVruOuuu3yOmabJihUraGxs5P333+fgwYPYbDYcDgcej8c77vLly2RmZvLSSy9d9xqtra04HA5iY2PZu3cvpaWl/Pbbb7z22mtDWJ7IyBaI3Ltqx44djBo16l+vV1xcTExMTEDXIDJSBSL/jh8/jtPpZObMmezZs4cDBw7gdDoJDw8HVPtErmeouefxeHA6nZimSVlZGRUVFfT19bF8+XIGBgauuZ5qn0iQmYOUmJho7t+/37t95swZ0263m6dOnfLu6+/vN9PS0sy9e/dec35tba1pt9vNc+fO+ezfvXu3OXPmTPPvv//27qurqzPtdrvZ2Ng42GmK3HaGknu1tbXmnDlzzPb2dtNut5tVVVXXxP/qq6/M+fPnm/X19abdbjdra2uDtxiREeZm8y87O9vcuHHjDeOq9on8u5vJvSNHjpiGYZjd3d3eMRcvXjQNwzC/++47n/iqfSLBN+TvcPb29gJgsVi8+0JDQ7FYLPz444+DihMeHu5zB+bqf7UGE0fkTuFv7v3555+sXr2aN998k/Hjx183VktLC+vXr2fDhg1EREQEd+IitwF/8q+jo4Njx44RFRXFc889x6xZs3j++eeprq72iaPaJ+I/f3Kvt7eXkJAQn3oWERFBaGioT16p9okMjyE3nHFxcdhsNt555x26u7vp7e1l27ZttLS00NbW5nectLQ0urq62LZtG729vVy4cIG3334bYFBxRO4U/ubeunXrmD17Ng8//PB14/T39/Pyyy/jdDqJj48frumLjGj+5N+5c+cAcLvdLFy4kO3bt5OSkoLL5aKurg5Q7RMZLH9yLzExkcjISEpKSvB4PHg8HoqLi+nv7/eOUe0TGT5DbjjDw8PZvHkzTU1NpKamkpiYyNGjR5kzZw6hof6Hv//++ykqKmLnzp0kJiaSkZGBzWZjwoQJg4ojcqfwJ/c+/fRTTp8+zSuvvHLDOFu3biUsLAyHwzFcUxcZ8fzJv6vfFcvOzmbRokVMmzaNVatWMWPGDCoqKgDVPpHB8if3rFYrmzZt4ptvviE5OZmUlBQuXrxIQkKCd4xqn8jwCQtEkOnTp1NZWcmlS5fo6+vDarXyzDPPMH369EHFycrKIisri/b2du6++25CQkIoKytj8uTJgZimyG3n/+VeTU0N9fX1JCUl+ZyXn5/Pzp07qaiooKamhh9++IGEhASfMdnZ2Tz++OPeuy0i4uv/5V9UVBQAU6ZM8TkvLi6O33//3but2icyOP587szMzOTrr7+ms7OTsLAwxo4dS0ZGhjevVPtEhk9AGs6rxowZA0BjYyMnTpwgLy/vpuJMmDABgH379hEREUFGRkbA5ihyO7pR7uXn5+N0On3GZmVl8eqrr/Loo48CUFhYyOXLl73H//jjD1wuFxs2bCA5OXmYViAyct0o/yZPnsx9993H2bNnfcY3NjZit9uviaPaJzI4/nzutFqtAFRXV9PR0cHcuXMB1T6R4eRXw9nT00NTUxPwzyNCzc3NnDp1inHjxjFp0iSqqqq49957sdlsnD59msLCQubNm0dmZqY3RltbG+3t7d7fSWpoaODSpUtMnDiRe+65B4Bdu3aRlJREZGQk33//PSUlJaxevZqxY8cGeNkiI8NQcy86Opro6Ohr4sbExBAbGwvg/XtVZGSkd79eEy93sqHmX0hICC6XC7fbjWEYTJs2jaqqKo4fP87atWu911HtE/EViM+d+/fvJy4ujvHjx3Ps2DEKCwvJyckhLi4OUO0TGU5+NZwnTpxg6dKl3m23243b7eapp56iqKiItrY2ioqK6OjoICoqiieffJIXX3zRJ8bu3bvZsmWLd3vZsmUAvPXWWzz99NPAPz+O7Xa76enpIS4ujjfeeIMFCxYMeZEiI1Ugck9Ebk4g8i8nJ4e+vj6Ki4vp7u5m6tSplJaW8sADD3jHqPaJ+ApE7p09e5aNGzdy4cIFbDYby5cvJycnZ5hXIiIAIaZpmrd6EiIiIiIiInL70SvwREREREREJCjUcIqIiIiIiEhQqOEUERERERGRoFDDKSIiIiIiIkGhhlNERERERESCQg2niIiIiIiIBIUaThEREREREQkKNZwiIiLXUVBQgGEYGIZBQkIC6enpLFmyhPLycvr6+vyOc/ToUQzDoLOzM4izFRER+W8Ku9UTEBER+a+aNWsWJSUlDAwM0NnZSU1NDZs3b6ayspKysjIiIyNv9RRFRET+03SHU0RE5AYsFgtRUVFER0cTHx+Pw+Hgk08+4ZdffmH79u0AVFZWsnDhQpKSkkhPT2flypW0trYCcP78eZYuXQpAeno6hmFQUFAAgGmalJaWMm/ePGbMmEFWVhaVlZW3ZqEiIiJBooZTRERkEOx2O5mZmXz55ZcA9PX1sXLlSj777DM+/PBDurq6WLVqFQATJ07E7XYDcOjQIb799lvWrFkDwLvvvsu+fftYu3Ythw4dYtmyZaxbt47Dhw/fknWJiIgEgx6pFRERGaSpU6dSXV0NwKJFi7z7Y2NjWb9+PfPnz6elpYWYmBjGjRsHgNVqxWq1AuDxePjoo4/YsWMHKSkp3nNra2spLy/nkUceGd4FiYiIBIkaThERkUEyTZOQkBAATp48yZYtW6irq6O7u9s7prm5mZiYmOueX19fz5UrV8jNzfXGgX/ultpstuBOXkREZBip4RQRERmkhoYGYmNj8Xg8uFwu78uFrFYrXV1dLF68+F/fZGuaJgAffPABkyZN8jkWFqbSLCIitw9VNRERkUH49ddfOXLkCC+88AJnzpyhq6uL/Px8YmNjAbzf7bwqPDwcgIGBAe++KVOmYLFYaG5uJj09ffgmLyIiMszUcIqIiNxAb28vbW1tDAwM0NXVRXV1NVu3biUhIQGn08lff/2FxWKhvLycxYsX09DQwKZNm3xi2Gw2QkJCOHz4MHPnziUiIoLRo0fjdDopKSnBNE0eeughPB4PP/30E6GhoWRnZ9+iFYuIiARWiHn1uR4RERHxKigo4ODBgwCMGjWKMWPGYLfbeeyxx8jOzsZisQDw+eefs3HjRlpbWzEMg7y8PHJzc/n4449JTU0F4L333qOiooL29nYWLFhAUVERpmmya9cuKioqaGpqYvTo0cTHx5Obm0tGRsYtW7eIiEggqeEUERERERGRoNDvcIqIiIiIiEhQqOEUERERERGRoFDDKSIiIiIiIkGhhlNERERERESCQg2niIiIiIiIBIUaThEREREREQkKNZwiIiIiIiISFGo4RUREREREJCjUcIqIiIiIiEhQ/A8sEbiaEMBDpQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "\n",
    "import arch.data.default\n",
    "\n",
    "default_data = arch.data.default.load()\n",
    "default = default_data.BAA.copy()\n",
    "default.name = 'default'\n",
    "default = default - default_data.AAA.values\n",
    "fig = default.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Default premium is clearly highly persistent.  A simple check of the autocorrelations confirms this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZNWvWVL169ax4SgAAAACwBMN6PXM171exCtTMzEzt3btXe/fuVW5uro4dO6a9e/fq2LFjkqQ5c+Zo2LBhru3vuece+fv7a/Lkydq/f78+/PBDJSQkMIMvAAAAAKBQxSpQd+/erT59+qhPnz66cOGCXn31VfXp00fz58+XJKWlpenIkSOu7StXrqxFixYpNTVV9913n/70pz9p5MiRGjFihDWvAgAAAADgeMWaJOnOO+/Ud999V+j6F198Md+y0NBQJSYmet8yAAAAALCpgCr+8i9v2Zyz+Zy/eFnnzp73eL/9+/fpoYceUHh4Ey1cuCjf+q++2qGVK5dpz57/6Pz5C7rpppvUuvWdGjRoqGrXrqOvvtqhJ54Yk2+//v0Ha9y4iV69liu5du/oVSrsP0BBM0B5+8sDAAAAgOLwL19Wt07eeM2e7/CLPXXOi/3WrVujvn1/rw8+2KjDh39QgwYNXOvWrHlXc+fOUpcu3fXcc7NUu3YdpaWlavPmTfp//+8tTZ483bXt0qV/c7ttjL+//9W8nEI5pkD15D+At788AAAAACgtLl68oI8++kALFryhCxcuaMOGtRo3boIkKTX1hP7855fVr19/jR//tGuf2rXrqFmzFvr555/dsqpVq67AwEDL22zJLL4AAAAAgOvr44+3qFat2rrjjobq2rWHPvhgoy5fvvS/6z7SpUuXNHTo8AL3rVy58HuVWskxZ1ABAAAAAMW3YcNade3aQ5LUsuXvVKFCBX366T8VE9NBR44cUaVKlRQUFFysrP7973F7vHTpKt10000l3mYKVAAAAAAoZY4ePaL//OdrPfvs85J+uTdp587dtG7dasXEdJBkPLoF6Pz5f1Xlyv93DWpQUFBJN1kSBSoAAAAAlDrr169RTk6O7ruvl2uZMUaSdOLEcdWvf7POnTun9PS0Yp1FrV27LtegAgAAAAA8c/nyZX3wwQY9/PDjWrw40fWzZMlyNWjQUElJ63X33R1Vrlw5LVu2pMCM306SdK1wBhUAAAAASpF//3ubTp8+rXvv7aOqVd3Penbu3FXvvbdKw4Y9qLFjJ2jevNk6d+6cevS4R3Xq1FV6epo2b/5A2dnZmjRp2jVvOwUqAAAAAHjo/MXLOvxiz2v6fMW1YcNatWoVka84laTY2E76y1/ma8eOz9WvX3/dfPMtWrlymaZNm6QLF86rVq2b1KZNWw0b9mBJNr/YKFABAAAAwEPnzp7Xed8yysnJLfFs36vMnTVrXqHr6tatp23bdrgeR0S0UUREm0K3b9Uqwm17q3ENKgAAAADAFm74M6gBVfzlX77gtyE42P3mtOcvXta5s+evRbMAAAAA4IZzwxeo/uXL6tbJG4u17eEXe+qcxe0BAAAAgBsVQ3wBAAAAALZAgQoAAAAAV2CMud5NcJSreb8oUAEAAACgEL6+ZXXpUvb1boajXLqULV9f764mpUAFAAAAgEIEBATq9Ok0ZWdf5ExqEYwxys6+qNOn0xQQkP8erMVxw0+SBAAAAACF8fevJEk6cyZdOTmX3db5+PhYUrRalWtldl6ur29ZVa5czfW+eYoCFQAAAACuwN+/UoEFV2BgRZ0+nVXiz2dVrpXZJZXLEF8AAAAAgC1wBtVCAVX85V8+/1scHFw537LzFy/r3Nnz16JZAAAAAGBLFKgW8i9fVrdO3lisbQ+/2FPnLG4PAAAAANgZQ3wBAAAAALZAgQoAAAAAsAUKVAAAAACALVCgAgAAAABsgQIVAAAAAGALzOLrQNy+BgAAAEBpRIHqQNy+BgAAAEBpxBBfAAAAAIAtUKACAAAAAGyBAhUAAAAAYAtcgwqXwiZfkvJPwMTkSwAAAABKGgUqXJh8CQAAAMD1xBBfAAAAAIAtUKACAAAAAGyBAhUAAAAAYAsUqAAAAAAAW2CSJFwThc0Q/NvZgSVmCAYAAABuVBSouCaYIRgAAABAURjiCwAAAACwBQpUAAAAAIAtUKACAAAAAGyBAhUAAAAAYAtMkgRHY3ZgAAAAoPSgQIWjMTswAAAAUHowxBcAAAAAYAsUqAAAAAAAW6BABQAAAADYAgUqAAAAAMAWKFABAAAAALbALL5AAQq7fY2U/xY23L4GAAAAKBnFLlATExP11ltvKS0tTQ0bNtTUqVMVERFR6Pbr16/Xm2++qcOHDysgIEDt2rXTpEmTFBwcXCINB6zE7WsAAACAa69YQ3yTkpI0c+ZMjRkzRmvWrFHLli01atQoHTt2rMDtv/zyS8XHx6tv377asGGDXnvtNR08eFBPPfVUiTYeAAAAAFB6FKtAXbx4sfr27asBAwaoQYMGmj59uoKDg7VixYoCt9+1a5duuukmDR8+XPXr11eLFi00dOhQffPNNyXaeAAAAABA6VFkgZqdna09e/YoMjLSbXlkZKR27txZ4D6tWrVSWlqatm7dKmOMTp48qaSkJMXExJRMqwEAAAAApU6RBeqpU6eUk5OjoKAgt+U1atRQWlpagfu0bNlSc+bM0VNPPaUmTZqoXbt2MsZo1qxZJdNqAAAAAECpU+xJknx8fIq1TJIOHDigGTNm6NFHH1VUVJTS0tI0e/Zs/eEPf9Ds2bOv+Dy+vj4KDKxY3GYVqiQyrmWuldlOy7Uy2665vr5lLGmbVblWZjst18psp+Vame20XCuznZZrZTa51mc7LdfKbKflWpnttFwrs52Wa2V2SeUWWaBWq1ZNvr6++c6WZmRk5Durmuf1119Xs2bN9NBDD0mSwsLC5O/vr7i4OD355JOqXbt2oc+Xk2N0+nRWvuW/vbVHUQrKKIhVuVZmOy3Xymyn5V7p9jVlyvjmW3a1t7AJDKzo0e/JDtlOy7Uy22m5VmY7LdfKbKflWplNrvXZTsu1MttpuVZmOy3Xymyn5VqZ7UnulY61iyxQ/fz8FB4eruTkZHXv3t21PDk5WV26dClwnwsXLsjX1/1gO++xMaZYjQZKI09uXyNxCxsAAADcWIo1i++IESO0evVqrVq1SgcPHtSMGTOUmpqqQYMGSZLi4+MVHx/v2r5Dhw7asmWLli9friNHjujLL7/UjBkzFB4erjp16ljzSgAAAAAAjlasa1B79OihU6dOaeHChUpNTVVISIgSEhJUt25dSVJKSorb9v369VNmZqYSExM1a9YsVa5cWXfeeaeefvrpkn8FAAAAAIBSodiTJMXFxSkuLq7AdUuXLs237P7779f999/vfcsAAAAAADeUYg3xBQAAAADAahSoAAAAAABbKPYQXwD2VtgtbAqaxvtqb18DAAAAWIECFSglPLmFDbevAQAAgB0xxBcAAAAAYAsUqAAAAAAAW6BABQAAAADYAgUqAAAAAMAWKFABAAAAALZAgQoAAAAAsAUKVAAAAACALXAfVABXFFDFX/7lC/6oCA6u7Pb4/MXLOnf2/LVoFgAAAEohClQAV+RfvqxunbyxWNsefrGnzlncHgAAAJReDPEFAAAAANgCBSoAAAAAwBYoUAEAAAAAtkCBCgAAAACwBQpUAAAAAIAtUKACAAAAAGyB28wAuC48ub+qxD1WAQAAbgQUqACuC0/urypxj1UAAIAbAUN8AQAAAAC2QIEKAAAAALAFClQAAAAAgC1QoAIAAAAAbIECFQAAAABgCxSoAAAAAABboEAFAAAAANgC90EFUOoEVPGXf/n8H2/BwZXzLTt/8bLOnT1/LZoFAACAIlCgAih1/MuX1a2TNxZr28Mv9tQ5i9sDAACA4mGILwAAAADAFihQAQAAAAC2QIEKAAAAALAFClQAAAAAgC0wSRIAFFNhswNL+WcIZnZgAAAAz1GgAkAxMTswAACAtRjiCwAAAACwBQpUAAAAAIAtUKACAAAAAGyBAhUAAAAAYAtMkgQA15knswNLzBAMAABKLwpUALjOPJkdWGKGYAAAUHoxxBcAAAAAYAucQQWAUqyw4cMMHQYAAHZEgQoApZgnw4cZOgwAAK43hvgCAAAAAGyBAhUAAAAAYAsM8QUAeMyTW+NwbSsAACguClQAgMe4thUAAFiBIb4AAAAAAFugQAUAAAAA2AIFKgAAAADAFrgGFQBgG55MviQxARMAAKVNsQvUxMREvfXWW0pLS1PDhg01depURUREFLp9dna2Fi5cqLVr1yo1NVVBQUEaOXKkHnjggRJpOACg9PFk8iWJCZgAAChtilWgJiUlaebMmfrjH/+o3/3ud1q+fLlGjRqljRs3qk6dOgXuM3HiRKWkpOi5557TLbfcooyMDF24cKFEGw8AAAAAKD2KVaAuXrxYffv21YABAyRJ06dP16effqoVK1Zo4sSJ+bbftm2bkpOTtXnzZlWvXl2SVK9evRJsNgAAAACgtClykqTs7Gzt2bNHkZGRbssjIyO1c+fOAvf56KOP1LRpUy1ZskQxMTHq0qWLZsyYoczMzJJpNQAAAACg1CnyDOqpU6eUk5OjoKAgt+U1atRQcnJygfscOXJEX375pfz8/PTqq6/q7NmzmjFjhlJTUzV//vwrPp+vr48CAyt68BIKVhIZ1zLXymyn5VqZ7bRcK7OdlmtlttNyrcx2Wu7VZvv6lrGsbVZlOy3Xymxyrc92Wq6V2U7LtTLbablWZjst18rsksot9iRJPj4+xVomScYY+fj4aM6cOapc+ZdZF6dPn64HH3xQ6enp+YrdX8vJMTp9Oivf8oJmb7ySgjIKYlWuldlOy7Uyu7TnWpnttFwrs52Wa2W203I9yS5IYGDFq9r/emQ7LdfKbHKtz3ZarpXZTsu1MttpuVZmOy3XymxPcq/U3xdZoFarVk2+vr5KS0tzW56RkVFooRkcHKxatWq5ilNJatCggSTp2LFjVyxQAQCwQmG3sOH2NQAA2EeRBaqfn5/Cw8OVnJys7t27u5YnJyerS5cuBe7TqlUrffDBB8rMzFSlSpUkSYcPH5Yk1a1btwSaDQCAZzy5hQ23rwEA4PoocpIkSRoxYoRWr16tVatW6eDBg67rSQcNGiRJio+PV3x8vGv7Xr16KTAwUFOmTNH333+vL7/8Us8//7y6du2qGjVqWPNKAAAAAACOVqxrUHv06KFTp05p4cKFSk1NVUhIiBISElxnQ1NSUty2r1SpkhYvXqwZM2bo97//vapUqaJOnToVeEsaAAAAAAAkDyZJiouLU1xcXIHrli5dmm/Z7bffrkWLFnnfMgAAAADADaVYQ3wBAAAAALAaBSoAAAAAwBaKPcQXAADkV9jta6T8t7Dh9jUAAFwZBSoAAFeB29cAAFByGOILAAAAALAFClQAAAAAgC1QoAIAAAAAbIECFQAAAABgC0ySBACADTE7MADgRkSBCgCADTE7MADgRsQQXwAAAACALVCgAgAAAABsgSG+AADcYAq7vvW317ZKXN8KALi2KFABALjBcH0rAMCuGOILAAAAALAFzqACAIASwa1xAABXiwIVAACUCIYOAwCuFkN8AQAAAAC2QIEKAAAAALAFhvgCAABb49pWALhxUKACAABb49pWALhxMMQXAAAAAGALFKgAAAAAAFtgiC8AALhhFXZ962+vbZW4vhUArgUKVAAAcMPi+lYAsBeG+AIAAAAAbIECFQAAAABgCwzxBQAAKGFc2woA3qFABQAAKGFc2woA3mGILwAAAADAFjiDCgAA4BCFDR2W8g8fZugwACeiQAUAAHAIhg4DKO0Y4gsAAAAAsAXOoAIAAICZhwHYAgUqAAAAGD4MwBYY4gsAAAAAsAXOoAIAAMAyDB0G4AkKVAAAAFiGocMAPMEQXwAAAACALXAGFQAAAI5T2NBhKf/wYYYOA85BgQoAAADHYegwUDoxxBcAAAAAYAucQQUAAAB+hZmHgeuHAhUAAAD4FYYPA9cPQ3wBAAAAALbAGVQAAADgGmDoMFA0ClQAAADgGmDoMFA0ClQAAADAwbgnLEoTClQAAADAwTgzi9KESZIAAAAAALbAGVQAAAAA+XgydFhi+DBKBgUqAAAAgHw8GTosMXwYJYMCFQAAAMA1xS13UJhiF6iJiYl66623lJaWpoYNG2rq1KmKiIgocr8dO3bogQce0O23364NGzZcVWMBAAAAOB8TO6EwxZokKSkpSTNnztSYMWO0Zs0atWzZUqNGjdKxY8euuAjJL9cAACAASURBVN+ZM2c0adIktWvXrkQaCwAAAAAovYpVoC5evFh9+/bVgAED1KBBA02fPl3BwcFasWLFFfd75pln1LdvX7Vo0aJEGgsAAAAAhQmo4q/g4Mr5fsqV8823LKCK//VuLgpQ5BDf7Oxs7dmzRyNHjnRbHhkZqZ07dxa6X2JiotLT0/XII4/oL3/5y9W3FAAAAACugKHDzldkgXrq1Cnl5OQoKCjIbXmNGjWUnJxc4D7fffedXnvtNb3zzjvy9fX1qEG+vj4KDKzo0T4FKYmMa5lrZbbTcq3MdlquldlOy7Uy22m5VmY7LdfKbHKtz3ZarpXZTsu1MttpuVZmOy3Xymy75vr6lrGkbVblWpldUrnFniTJx8enWMuys7M1YcIExcfHq379+h43KCfH6PTprHzLC5rR60oKyiiIVblWZjst18rs0p5rZbbTcq3MdlquldlOy7Uyu7TmWpnttFwrs52Wa2W203KtzC7tuVZmX+/cwgQGVrzqjGuZa2W2J7lX+j0VWaBWq1ZNvr6+SktLc1uekZGR76yqJKWmpurAgQOaOnWqpk6dKknKzc2VMUaNGzdWQkKCoqKiitVwAAAAALjeCrstjsStcUpakQWqn5+fwsPDlZycrO7du7uWJycnq0uXLvm2r1WrltavX++2bPny5UpOTtaCBQtUt27dEmg2AAAAAFwbnlzbKnF969Uo1hDfESNGKD4+Xs2aNVOrVq20YsUKpaamatCgQZKk+Ph4SdLs2bNVrlw5hYSEuO1fo0YN+fn55VsOAAAAADeyws7O3qhnZotVoPbo0UOnTp3SwoULlZqaqpCQECUkJLjOhqakpFjaSAAAAAAojZh52F2xJ0mKi4tTXFxcgeuWLl16xX3Hjh2rsWPHetYyAAAAAMANpdgFKgAAAADAGTyZ2MlOQ4cpUAEAAACglHHq0OEy17sBAAAAAABInEEFAAAAABST1feEpUAFAAAAABSL1feEZYgvAAAAAMAWKFABAAAAALZAgQoAAAAAsAUKVAAAAACALVCgAgAAAABsgQIVAAAAAGALFKgAAAAAAFugQAUAAAAA2AIFKgAAAADAFihQAQAAAAC2QIEKAAAAALAFClQAAAAAgC1QoAIAAAAAbIECFQAAAABgCxSoAAAAAABboEAFAAAAANgCBSoAAAAAwBYoUAEAAAAAtkCBCgAAAACwBQpUAAAAAIAtUKACAAAAAGyBAhUAAAAAYAsUqAAAAAAAW6BABQAAAADYAgUqAAAAAMAWKFABAAAAALZAgQoAAAAAsAUKVAAAAACALVCgAgAAAABsgQIVAAAAAGALFKgAAAAAAFugQAUAAAAA2AIFKgAAAADAFihQAQAAAAC2QIEKAAAAALAFClQAAAAAgC1QoAIAAAAAbIECFQAAAABgCxSoAAAAAABboEAFAAAAANgCBSoAAAAAwBYoUAEAAAAAtkCBCgAAAACwBQpUAAAAAIAtUKACAAAAAGyBAhUAAAAAYAsUqAAAAAAAWyh2gZqYmKjY2Fg1bdpU/fr1044dOwrd9sMPP9TIkSPVtm1btWzZUv3799eWLVtKpMEAAAAAgNKpWAVqUlKSZs6cqTFjxmjNmjVq2bKlRo0apWPHjhW4/eeff662bdsqISFBa9asUfv27fX4449fsagFAAAAANzYilWgLl68WH379tWAAQPUoEEDTZ8+XcHBwVqxYkWB20+bNk2jR49Ws2bNdMstt+jxxx9XeHi4PvrooxJtPAAAAACg9CiyQM3OztaePXsUGRnptjwyMlI7d+4s9hNlZmaqSpUqnrcQAAAAAHBDKFvUBqdOnVJOTo6CgoLclteoUUPJycnFepLExEQdP35cvXv3LnJbX18fBQZWLFbulZRExrXMtTLbablWZjst18psp+Vame20XCuznZZrZTa51mc7LdfKbKflWpnttFwrs52Wa2W203KtzHZarqfZRRaoeXx8fIq17Lc2bdqk2bNna+7cuapbt26R2+fkGJ0+nZVveXBw5eI19H8VlFEQq3KtzHZarpXZpT3Xymyn5VqZ7bRcK7OdlmtldmnNtTLbablWZjst18psp+VamV3ac63MdlquldlOyy0o+0oZRQ7xrVatmnx9fZWWlua2PCMjI99Z1d/atGmT4uPjNWvWLHXs2LGopwIAAAAA3MCKLFD9/PwUHh6ebzhvcnKyWrZsWeh+SUlJevrpp/XCCy+oW7duV99SAAAAAECpVqwhviNGjFB8fLyaNWumVq1aacWKFUpNTdWgQYMkSfHx8ZKk2bNnS5I2btyo+Ph4xcfHq3Xr1q6zr+XKlVNgYKAVrwMAAAAA4HDFKlB79OihU6dOaeHChUpNTVVISIgSEhJc15SmpKS4bb9y5UpdvnxZM2fO1MyZM13L27Rpo6VLl5Zg8wEAAAAApUWxJ0mKi4tTXFxcget+W3RShAIAAAAAPFXkNagAAAAAAFwLFKgAAAAAAFugQAUAAAAA2AIFKgAAAADAFihQAQAAAAC2QIEKAAAAALAFClQAAAAAgC1QoAIAAAAAbIECFQAAAABgCxSoAAAAAABboEAFAAAAANgCBSoAAAAAwBYoUAEAAAAAtkCBCgAAAACwBQpUAAAAAIAtUKACAAAAAGyBAhUAAAAAYAsUqAAAAAAAW6BABQAAAADYAgUqAAAAAMAWKFABAAAAALZAgQoAAAAAsAUKVAAAAACALVCgAgAAAABsgQIVAAAAAGALFKgAAAAAAFugQAUAAAAA2AIFKgAAAADAFihQAQAAAAC2QIEKAAAAALAFClQAAAAAgC1QoAIAAAAAbIECFQAAAABgCxSoAAAAAABboEAFAAAAANgCBSoAAAAAwBYoUAEAAAAAtkCBCgAAAACwBQpUAAAAAIAtUKACAAAAAGyBAhUAAAAAYAsUqAAAAAAAW6BABQAAAADYAgUqAAAAAMAWKFABAAAAALZAgQoAAAAAsAUKVAAAAACALVCgAgAAAABsgQIVAAAAAGALFKgAAAAAAFugQAUAAAAA2AIFKgAAAADAFihQAQAAAAC2UOwCNTExUbGxsWratKn69eunHTt2XHH7zz//XP369VPTpk3VsWNHrVix4qobCwAAAAAovYpVoCYlJWnmzJkaM2aM1qxZo5YtW2rUqFE6duxYgdsfOXJEo0ePVsuWLbVmzRo9/PDDmjFjhjZt2lSijQcAAAAAlB7FKlAXL16svn37asCAAWrQoIGmT5+u4ODgQs+Krly5UjVr1tT06dPVoEEDDRgwQH369NGiRYtKtPEAAAAAgNKjyAI1Oztbe/bsUWRkpNvyyMhI7dy5s8B9du3alW/7qKgo7d69W5cuXbqK5gIAAAAASisfY4y50gYnTpxQTEyMli1bptatW7uWL1iwQOvXry9w2G7Xrl11zz336PHHH3ct++KLLzR06FB9+umnqlmzZgm+BAAAAABAaVDsSZJ8fHyKtaywdXl18JX2AQAAAADcuIosUKtVqyZfX1+lpaW5Lc/IyFBQUFCB+wQFBSk9PT3f9mXLllVgYOBVNBcAAAAAUFoVWaD6+fkpPDxcycnJbsuTk5PVsmXLAvdp0aJFgds3adJE5cqVu4rmAgAAAABKq2IN8R0xYoRWr16tVatW6eDBg5oxY4ZSU1M1aNAgSVJ8fLzi4+Nd2w8aNEgnTpzQ888/r4MHD2rVqlVavXq1Ro4cac2rAAAAAAA4XtnibNSjRw+dOnVKCxcuVGpqqkJCQpSQkKC6detKklJSUty2r1+/vhISEvTCCy9oxYoVqlmzpp555hl17dq15F8BAAAAAKBUKHIWXwAAAAAAroViz+ILAAAAAICVKFBLiUuXLl3vJgAAAADAVWGIbynRpEkTrV27Vg0aNLjeTUERUlNTtWLFCn355ZdKS0uTr6+v6tWrp44dO6pfv37y9fW93k0EAAAArotSU6CmpKRo/vz5euGFFzze9+zZs/rqq69UpUoVtWzZUj4+Pq51WVlZWrRokR5//HGPc/fv369du3apZcuWatiwoQ4cOKAlS5YoOztb9957r6KiojzOnDFjRoHLExMT1bNnT9d9ZqdNm+Zx9m+dOXNGq1ev1o8//qjg4GD17dtXtWvX9jhnx44dql69um6//XZXW5cvX65jx46pbt26iouL0+DBg71q45gxY9S9e3d169ZN5cuX9yqjILm5uXr99df19ddf6+6779agQYP07rvvKiEhQbm5uercubPGjx8vPz8/j3L/85//aMSIEbr55ptVoUIF7dq1S7169dKlS5e0bds2NWjQQG+++aYCAgJK7LUAsF5WVpY2bNignTt3Ki0tTT4+PgoKClKrVq3Us2dPVaxYscSfMz09XStXrvSqf8rNzdXBgwdVpUoV1apVy23dxYsX9f7776tPnz5etevkyZPau3evGjVqpOrVqys9PV2rVq1Sdna2unfvrpCQEK9yC3L33XdryZIluvXWW0sk79KlS/rkk090+PBhBQcHq3Pnzl797g4dOqRKlSq53ttPPvlEiYmJSklJUZ06dRQXF6eYmBiv2vjcc8+pe/fuioiI8Gr/K1m3bp2++eYbRUdHq3379tq2bZsWLVrk6vfi4uK8yr1w4YI2bNiQ74vZTp06qV27diX8KgBcC1b2e6WmQN23b5/69u2rvXv3erTf999/rxEjRujkyZPKzc1V48aN9eqrr7pmKE5PT1d0dLTHuZ988okee+wxVapUSVlZWVqwYIEmTZqkRo0aKTc3V1988YXefPNN3XXXXR7lhoWFKSwsTJUrV3Zb/sUXX6hJkyby9/eXj4+P3n77bY9yJSkqKkrr169XtWrVdOTIEQ0ePFi5ubm64447dOjQIV24cEHvvPOOx2dpe/XqpWnTpqlt27ZKTEzUyy+/rAceeEC33367fvjhBy1btkxPPvmkVx1fWFiYfHx8VLlyZd17773q37+/QkNDPc75rVdeeUXLly9XbGystm/frr59+2r58uUaPny4ypQpoyVLlmjgwIEaP368R7mDBw9WZGSk64By7dq1SkxM1N/+9jedOXNGw4YNU0REhNdfMDjtIFmy7kDZyQfJkv0PlJ14kCxZc6B84MABjRgxQpmZmWrdurVq1KghY4xOnjypHTt2qFKlSlq0aJHuuOMOr9tdEG/7vZSUFI0aNUoHDhyQj4+PYmNjNXPmTFWtWlWS9/2eJO3cuVMPPfSQMjMzVblyZS1atEjjxo1TuXLllJubqxMnTigxMVFNmzb1KHfx4sUFLn/ppZc0fPhwBQcHS/rltnieGDRokBISElSlShWdPHlSw4YN0w8//KBatWrpxIkTCg4O1sqVK/N9NhWlX79+Gj9+vGJiYpSUlKSnn35a3bp1U4MGDXT48GElJSVp9uzZ6tGjh0e50v/1e7feeqsGDhyo3r17q1q1ah7n/NaSJUs0Z84ctWjRQvv27dNTTz2lF198UT179lSZMmW0du1aPfnkkxo+fLhHuT/++KNGjBihCxcuyM/PT8ePH1f79u116tQp7d69W507d9acOXNUtmyxbiyRj9P6Pb4cKlhJ9XkS/d5vObLfMw6xevXqK/689tprJiwszOPchx9+2Dz22GMmMzPTnDhxwjzxxBMmOjra/PDDD8YYY9LS0rzKHThwoJk7d64xxpgNGzaY1q1bux4bY8zLL79sRowY4XHuwoULTWxsrNm+fbvb8saNG5vvv//e47xfCw0NNenp6cYYY5588kkzdOhQk5mZaYwx5sKFC2b06NFm7NixHuc2bdrUHD161BhjTO/evc17773ntj4pKcl07drV6zZ/++235i9/+Yvp2LGjCQsLM/379zerVq1ytd0bsbGxZuvWrcYYY77//nsTFhZm1q5d61r/4Ycfmk6dOnmc26xZM/Pf//7X9TgnJ8eEh4ebtLQ0Y4wx27ZtM1FRUV61+fvvvzdRUVGmZcuWZvTo0WbKlClm8uTJZvTo0aZVq1YmOjr6qv+PFGTv3r1e/Y0YY8yxY8dMz549TWhoqAkLCzOPPvqoOX36tGu9t39/X331lWnVqpUJDQ01ERER5ptvvjEdOnQwXbp0MZ06dTJNmzY133zzjce5ixYtKvCnUaNGZtasWa7H3hg4cKA5c+aMMcaYjIwM06tXLxMeHm5iY2NNeHi4ufvuu83x48c9zu3bt6/55JNPjDHGbNy40TRu3NhMmDDBvPbaa+bpp5824eHhZuPGjR7n5v3OunXrZhYvXmxOnjzpcUZBFi9ebJo0aWKGDh1qIiIizMqVK02LFi3MM888Y6ZPn26aNWtmFi9e7FX24cOHTYcOHUy7du1M+/btTWhoqBk9erTp37+/adSokXniiSfMpUuXPM4dOnSoGTdunLlw4UK+dRcuXDDjx483Q4cO9Tj3888/v+LP3/72N6/+PiZMmGCGDBliDhw4YHbu3GkGDhxoevXqZTIyMowx3v/dGWPMsGHDzDPPPGN+/vln8+abb5qYmBjzzDPPuNZPnjzZPProox7nhoaGmpiYGNOhQwe3n9DQUBMdHW06dOhgYmNjvcrN6/emTZtm7r33XnPixAljzC9/hwMHDjRTpkzxOLd58+bmyJEjxhhj7rvvvnz/Z9955x1z7733epyb1+aPP/7YPPPMM6Zly5amSZMm5sknnzTJycle5eXp2rWrWbNmjTHGmC+//NKEh4ebZcuWuda/++67pnv37h7nPvTQQ2b69OkmNzfXGGPM66+/bh566CFjjDE//PCD6dChg5k/f75XbXZav2dVn2eM8/o9q/o8Y+j3fs1p/V4exxSooaGhpkWLFoX+NG/e3Ks/6rZt25r9+/e7LZs5c6aJiooyhw4d8vrDolWrVubw4cPGmF+KkMaNG5vdu3e71n/33Xfmrrvu8jjXGGN27txpOnXqZObMmWMuX75sjCn5AjU2NjZfZ7dr1y4TExPjcW7btm3Nf/7zH2OMMe3atTN79+51W//jjz+aZs2aXXWbjTHm008/NWPHjjXh4eGmVatWZvr06a7n9kTTpk3NTz/95HocHh7u9v/k6NGjpnnz5h7ndujQwXzxxReux8ePHzehoaHm/Pnzxhhjjhw5Ypo2bepxrjHOO0g2xroDZacdJOdlO+lA2WkHycZYd6DcrFmzK37+fvfdd159xuUdDIWGhhb6483fR2RkpNuBanZ2tnniiSdM9+7dTXp6+lUdJLdu3docOHDAlRsWFma+/vpr1/rdu3eb6Ohoj3OnTZtm+vTpYw4ePOi2/Gr7vl//3XXp0sV8/PHHbuu3b99uOnTo4HFuRESEq69r27Ztgf2eN33Ib9ucmZlpVq5cae677z4TGhpqOnbsaF5//XWTmprqcW6zZs3y9Xvfffed6/GRI0e8anPz5s1dX/obY8zFixdNeHi46+B+8+bNXr3Hxjiv3+PLIfdcK/o8Y+j3fs1p/V4exxSo0dHRZtOmTYWu//bbb70uJAt6g59//nkTGRlptm/f7nXur8+UtWjRwu3x0aNHvS5EjDHm7NmzZty4caZfv37m0KFDJVag5n1IRkdHu3VMxvzSOTVp0sTj3EmTJpnJkycbY4wZP36825lkY345K3w13yT/ukDNk5GRYRISEkyXLl28+v3Fxsaaf/zjH8YYYw4ePGjCwsJMUlKSa/0//vEPrzrUGTNmmB49epitW7eabdu2mbi4OLfO85NPPvHqzKwxzjtINsa6A2WnHSQb47wDZacdJBtj3YFyVFSU2bx5c6HrP/zwQ69GRrRt29asXbvWnDx5ssAfb/unFi1auL0Pxhhz+fJlM3bsWNOtWzev+9O87LwDw7zHv+77jh075nXf9/7775uYmBizcuVK17KSKFDz+r127drl+8L66NGjXvV7jz/+uJk1a5YxxpgHH3zQLFmyxG39O++8Y7p06eJ1mwvq97799lvzxz/+0fzud78z4eHhHufGxMSYzz//3BhjTEpKigkNDXX1g8YY89lnn3n1JXVUVJTbF8WnT582oaGh5ueffzbGGPPf//7Xq/fYGOf1e3w59H+s6vOMod/7Naf1e3m8G/B/HYSHh2vPnj3q0qVLget9fHxkvLic9rbbbtPu3bvzjZGeOnWqcnNz9eijj3rV3rp16+rw4cOqX7++JOmdd95xm2AoJSVFQUFBXmVLUuXKlfXKK6/ob3/7m4YMGaLc3Fyvs35t6NCh8vX11c8//6xDhw65Xa+QkpLi1XUuEydO1ODBgzVkyBA1b95cS5Ys0RdffKEGDRrohx9+0K5du/Taa6+VSPvzVK9eXaNGjdKoUaP02Wefebz/Pffco/j4eMXGxuqzzz7T6NGjNXv2bGVkZMjHx0dvvPGGunbt6nHu+PHjlZaWpscff1w5OTlq0aKFXnrpJdf6MmXKaMKECR7nSlKVKlV0+PDhQsf7//jjj6pSpYrHudWqVdOUKVMUHR1d4Pr9+/d7fE1Snrzr1PKUK1dOc+fO1ZNPPqmhQ4dq7ty5XuVeunTJNWlWuXLlVKFCBbf/u9WrV9fp06c9zn3uuef0wQcfaMSIEXr00Uc1cOBAr9pXmLwJ2n7++WfXdfB56tWrp7S0NI8z27Ztq3Xr1iksLEzh4eH67LPPFBYW5lq/fft2j6+v+62KFStq4MCBGjhwoPbu3at33nlHCQkJmj9/vnbv3u1RVmBgoH766SfVqVNHx48f1+XLl5WSkuL6LDp27JjrWklPVa5cWefOnXM9Pn/+vC5fvqxy5cpJkkJDQ716jwcMGKBJkybp4Ycf1l133aWgoCD5+PgoLS1NycnJSkhI8OpvpHHjxjpy5Eihn7tVq1b1qt+rX7++9u3b53btmK+vr+bNm6fx48drzJgxHmfmuemmm3T06FHVq1dPkjRv3jzX9aGSlJaW5prMz1PdunVT06ZNNXHiRH3yySd6/vnnvW7nrz399NMqV66cLl++rKNHj6phw4Zu7fXmc3PChAkaMmSI0tLS1Lp1a73yyivavXu3q99LSkrSc88951V7fz2R4681atRIzz77rCZPnqykpCSPczt16qSpU6eqd+/e2rp1q/r166cXX3xRubm5KlOmjF5++WVFRkZ6nBsZGamZM2fq2WeflZ+fn+bOnatGjRq5JgM8duyYatSo4XGu5Lx+z6o+T3Jmv2dFnyfR7/2a0/q9PI4pUB988EFlZmYWuv7mm2/2amKgzp07a8OGDQVekD5t2jTl5ORoxYoVHucOHDjQ7d6kv70w/ZNPPtGdd97pce5vDRgwQK1bt9auXbt00003XVXWby/2r1SpktvjrVu3enVheHBwsFavXq033nhDW7ZskTFG33zzjY4fP66WLVtqxYoVHk+YkadOnToqU+bKt/P15n1+4oknXLPsDho0SKNHj1ZISIheeuklnT9/XrGxsRo3bpzHuZUqVdIrr7yiixcv6vLly/neY29mds7jtINkyboDZSceJEvOOlB22kGyZN2B8tixY1W+fHm9/fbbmjt3ruu9McYoKChIDz/8sEaNGuVx7qBBg5SVlVXo+tq1a3s1c310dLRWrVqlbt26uS3P+9t74oknlJqa6nGu9Mvfx68Pdu6++2639Vu3blWzZs28ypZ++fI3MTFR8+fPV+/evb3+7MnTt29f1787duyo8+fPu63ftGmT24Ftcd12221atWqV5s2bp9dff13nz5/X+vXrVbZsWTVp0kTz5s1Tp06dvGpzUa+5QoUK6tevn8e5EydOVHZ2tjZt2qRWrVpp2rRpWrp0qcaOHavLly+rdevWmjhxose5Tz/9tB599FHde++98vHxUe3atbVgwQLX+lOnTunBBx/0OFdyXr/Hl0PurOjzJPq9X3Nav5en1MziC0BKSEjQ22+/rfT09HwfFsOGDfPqw2Lz5s3KyspS7969C1x/5swZbd261e1Ar7heeukl7du3T2+99Va+dZcvX9YTTzyhrVu3at++fR7l/vnPf9btt9+ue+65p8D1r7zyig4cOOB2kOSpnJwczZ8/X6tXr1Z6errWrVt3VbO0Tpkyxe1xdHS02wyfs2bN0v79+wt8r4py9OhRzZs3Tx9//LGr4Mk7UH7ooYe8OlAOCwvTv/71L6/PfBQmKytLL7zwgnbt2uV2kDx37lzXQfIrr7zi1fNmZGTo0Ucf1ddff+12oNy4cWNJ0gcffKC0tDTdf//9Xrf/yJEjSk9PlyQFBQW5RtHYyeXLl3XhwoVCb2eVk5Oj48eP5zujURLOnTunsmXLqkKFCled9fnnn+vzzz/XkCFDVL169RJoXX5ZWVny9fW9qtuYGWOUkZGh3NxcVatWzXXmwikuXryoS5cuXfXtzw4fPqzs7GzdfvvtXs/YWxAn9XvF6fM+/vhjr2bQdlq/Z2WfJ/3yWfzKK6/Q713jfi8wMFC33Xab11l5KFCBUsgJB8nS9TtQdtpBssSBckkdJEvWHSgDuH6c0O/x5VDxlUSfJ9Hv5blW/V6TJk20du1aj29J+Vu+zz777LMl0yQAdlG1alXVrl1btWvXdl23kJKSopkzZ3o9rKwwV5NbpkwZ+fn5Fbr+xIkTevXVV0u8zRkZGZo9e3aJ5NatW1dt2rSRv7+/Ze+x9Mt992bNmnVV2T4+PqpYsaIqVaokX19fSfb8f1GQsmXLys/Pr0RyAwMDVaPG/2/v/kLZ3+M4jr+58GcLNWuNpLj5Nt/VlovRJjdcuCIpmjYpd3JhFy4m7pBkwo0UN24kJTfKDc0ipSQhWdKuzBX5X2Lvc3H6rfn5cY7vfDr77LwetQutnt59cjPbPu/CD18PSKZ9d3dHu7u7dH19TWaz+d1HwZ6enmh2dpYcDkfad2WcWbaujDOLPItwOEwbGxtkMplIVVV6fHyk+fl5Wl9fp9zcXCotLU2qm5WVRYWFhXR+fk4TExNJdTMzMykSiXza1ev1ZLVaNc37TzMXFBRQeXn5j3Sfn59pe3ubtra2fuSMOkE4pwAAA3JJREFUs7OzyWAwvJs3Pz9f87yJ7ZycHCopKaFoNEpTU1Mp+XeR2E08i+npadrc3Eyq+6u9v79PxcXFZDQaf2TmoaEhCoVCHx6Hh4d0e3tLe3t7FAqFNO2bJSJ59qACQHKS2Vf6X3RFtmXrimyjm3w7HA6zy+Vii8XCiqJwc3NzfPczs/bVEbJ1ZZxZtq6MM4s8i2AwyKqqssPhYKvVysFgkKuqqrizs5M7OjrYYrHwzs5O2ndlnBlnIb4rsq0oCjc1NbHH43n3UBSFW1pa2OPxsNfr1TQzs0S3+ALA11ZXV798/vLyMqW6ItuydUW20RXfDgQCZLfbaWxsjB4eHmh4eJjcbjctLCy8uwwl3bsyzixbV8aZRZ7FzMwMdXV1kc/no7W1Nerr6yO3200+ny/+u+fm5sjpdKZ1V8aZcRbiuyLbvb29tLy8TH6//91lpKqq0ujoaFJ3chAR3kEFSBeKorDdbv/0YbPZNP2XWlRXxplxFvJ2Rbarq6s/7M8cGRnhmpoavri40PwOkWxdGWeWrSvjzCLPorKykiORCDMzv729cUVFBR8fH8efPzs7Y6fTmfZdGWfGWYjvim4fHBxwfX09BwIBfn19Zeaf2QvPjHdQAdKGyWSigYGBT3cFn56ealo9IKorsi1bV2QbXfHtl5eXD+sH/H4/MTN5vV4KBAKa5pWtK+PMsnVlnFnkWRBR/Lvkv+40SFxNotfr6f7+/n/RlXFmnIX4rsi23W6nlZUVGhwcpNbWVhofH9c84+++XiAJANJQVZVOTk4+fT4jI0PT3jZRXZFt2boi2+iKb5eVlf1xMXt/fz81NDRQd3f3t5sydkW20RXflq1L9PcldZFIJP7z0tISFRUVxX+ORqNkNBrTvivjzDgL8V3RbSKivLw8mpycpLa2Nmpvb6dYLKa5lQi3+AKkCbPZTEaj8dPv9Oh0OnK5XN++vl5UV2Rbtq7INrri2zc3NxQMBqmxsfHDc7W1tXR1dUVHR0fU09OT1l0ZZ5atK+PMIs8iFouRTqeL7138/XbuxcVFMhgM376ZW7aujDPjLMR3RbcTqapKdXV1pKoq2Wy2Lzc0/BvYgwoAAAAAAAApAR/xBQAAAAAAgJSAF6gAAAAAAACQEvACFQAAAAAAAFICXqACAAAAAABASsALVAAAAAAAAEgJfwEYkHlN8hDGrQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "acf = pd.DataFrame(sm.tsa.stattools.acf(default), columns=['ACF'])\n",
    "fig = acf[1:].plot(kind='bar', title='Autocorrelations')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Augmented Dickey-Fuller Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Augmented Dickey-Fuller test is the most common unit root test used.  It is a regression of the first difference of the variable  on its lagged level as well as additional lags of the first difference.  The null is that the series contains a unit root, and the (one-sided) alternative is that the series is stationary. \n",
    "\n",
    "By default, the number of lags is selected by minimizing the AIC across a range of lag lengths (which can be set using `max_lag` when initializing the model).  Additionally, the basic test includes a constant in the ADF regression.\n",
    "\n",
    "These results indicate that the Default premium is stationary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Augmented Dickey-Fuller Results   \n",
      "=====================================\n",
      "Test Statistic                 -3.356\n",
      "P-value                         0.013\n",
      "Lags                               21\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant\n",
      "Critical Values: -3.44 (1%), -2.86 (5%), -2.57 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "from arch.unitroot import ADF\n",
    "\n",
    "adf = ADF(default)\n",
    "print(adf.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of lags can be directly set using `lags`.  Changing the number of lags makes no difference to the conclusion.\n",
    "\n",
    "**Note**: The ADF assumes residuals are white noise, and that the number of lags is sufficient to pick up any dependence in the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setting the number of lags"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Augmented Dickey-Fuller Results   \n",
      "=====================================\n",
      "Test Statistic                 -3.582\n",
      "P-value                         0.006\n",
      "Lags                                5\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant\n",
      "Critical Values: -3.44 (1%), -2.86 (5%), -2.57 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "adf.lags = 5\n",
    "print(adf.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Deterministic terms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The deterministic terms can be altered using `trend`.  The options are:\n",
    "\n",
    "* `'nc'` : No deterministic terms\n",
    "* `'c'` : Constant only\n",
    "* `'ct'` : Constant and time trend\n",
    "* `'ctt'` : Constant, time trend and time-trend squared\n",
    "\n",
    "Changing the type of constant also makes no difference for this data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Augmented Dickey-Fuller Results   \n",
      "=====================================\n",
      "Test Statistic                 -3.786\n",
      "P-value                         0.017\n",
      "Lags                                5\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant and Linear Time Trend\n",
      "Critical Values: -3.97 (1%), -3.41 (5%), -3.13 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "adf.trend = 'ct'\n",
    "print(adf.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ADF uses a standard regression when computing results.  These can be accesses using `regression`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.095\n",
      "Model:                            OLS   Adj. R-squared:                  0.090\n",
      "Method:                 Least Squares   F-statistic:                     17.83\n",
      "Date:                Sat, 25 Apr 2020   Prob (F-statistic):           1.30e-22\n",
      "Time:                        08:17:31   Log-Likelihood:                 630.15\n",
      "No. Observations:                1194   AIC:                            -1244.\n",
      "Df Residuals:                    1186   BIC:                            -1204.\n",
      "Df Model:                           7                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Level.L1      -0.0248      0.007     -3.786      0.000      -0.038      -0.012\n",
      "Diff.L1        0.2229      0.029      7.669      0.000       0.166       0.280\n",
      "Diff.L2       -0.0525      0.030     -1.769      0.077      -0.111       0.006\n",
      "Diff.L3       -0.1363      0.029     -4.642      0.000      -0.194      -0.079\n",
      "Diff.L4       -0.0510      0.030     -1.727      0.084      -0.109       0.007\n",
      "Diff.L5        0.0440      0.029      1.516      0.130      -0.013       0.101\n",
      "const          0.0383      0.013      2.858      0.004       0.012       0.065\n",
      "trend      -1.586e-05   1.29e-05     -1.230      0.219   -4.11e-05    9.43e-06\n",
      "==============================================================================\n",
      "Omnibus:                      665.553   Durbin-Watson:                   2.000\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):           146083.295\n",
      "Skew:                          -1.425   Prob(JB):                         0.00\n",
      "Kurtosis:                      57.113   Cond. No.                     5.70e+03\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 5.7e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "reg_res = adf.regression\n",
    "print(reg_res.summary().as_text())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "resids = pd.DataFrame(reg_res.resid)\n",
    "resids.index = default.index[6:]\n",
    "resids.columns = ['resids']\n",
    "fig = resids.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the number lags was directly set, it is good to check whether the residuals appear to be white noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "acf = pd.DataFrame(sm.tsa.stattools.acf(reg_res.resid), columns=['ACF'])\n",
    "fig = acf[1:].plot(kind='bar', title='Residual Autocorrelations')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dickey-Fuller GLS Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Dickey-Fuller GLS test is an improved version of the ADF which uses a GLS-detrending regression before running an ADF regression with no additional deterministic terms.  This test is only available with a constant or constant and time trend (`trend='c'` or  `trend='ct'`).\n",
    "\n",
    "The results of this test agree with the ADF results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      Dickey-Fuller GLS Results      \n",
      "=====================================\n",
      "Test Statistic                 -2.322\n",
      "P-value                         0.020\n",
      "Lags                               21\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant\n",
      "Critical Values: -2.59 (1%), -1.96 (5%), -1.64 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "from arch.unitroot import DFGLS\n",
    "\n",
    "dfgls = DFGLS(default)\n",
    "print(dfgls.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The trend can be altered using `trend`.  The conclusion is the same. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      Dickey-Fuller GLS Results      \n",
      "=====================================\n",
      "Test Statistic                 -3.464\n",
      "P-value                         0.009\n",
      "Lags                               21\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant and Linear Time Trend\n",
      "Critical Values: -3.43 (1%), -2.86 (5%), -2.58 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "dfgls.trend = 'ct'\n",
    "print(dfgls.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Phillips-Perron Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Phillips-Perron test is similar to the ADF except that the regression run does not include lagged values of the first differences.  Instead, the PP test fixed the t-statistic using a long run variance estimation, implemented using a Newey-West covariance estimator.  \n",
    "\n",
    "By default, the number of lags is automatically set, although this can be overridden using `lags`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Phillips-Perron Test (Z-tau)    \n",
      "=====================================\n",
      "Test Statistic                 -3.898\n",
      "P-value                         0.002\n",
      "Lags                               23\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant\n",
      "Critical Values: -3.44 (1%), -2.86 (5%), -2.57 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "from arch.unitroot import PhillipsPerron\n",
    "\n",
    "pp = PhillipsPerron(default)\n",
    "print(pp.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is important that the number of lags is sufficient to pick up any dependence in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Phillips-Perron Test (Z-tau)    \n",
      "=====================================\n",
      "Test Statistic                 -4.024\n",
      "P-value                         0.001\n",
      "Lags                               12\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant\n",
      "Critical Values: -3.44 (1%), -2.86 (5%), -2.57 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "pp.lags = 12\n",
    "print(pp.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The trend can be changed as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Phillips-Perron Test (Z-tau)    \n",
      "=====================================\n",
      "Test Statistic                 -4.262\n",
      "P-value                         0.004\n",
      "Lags                               12\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant and Linear Time Trend\n",
      "Critical Values: -3.97 (1%), -3.41 (5%), -3.13 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "pp.trend = 'ct'\n",
    "print(pp.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, the PP testing framework includes two types of tests. One which uses an ADF-type regression of the first difference on the level, the other which regresses the level on the level.  The default is the `tau` test, which is similar to an ADF regression, although this can be changed using `test_type='rho'`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Phillips-Perron Test (Z-rho)    \n",
      "=====================================\n",
      "Test Statistic                -36.114\n",
      "P-value                         0.002\n",
      "Lags                               12\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant and Linear Time Trend\n",
      "Critical Values: -29.16 (1%), -21.60 (5%), -18.17 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "pp.test_type = 'rho'\n",
    "print(pp.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## KPSS Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The KPSS test differs from the three previous in that the null is a stationary process and the alternative is a unit root.  \n",
    "\n",
    "Note that here the null is rejected which indicates that the series might be a unit root."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    KPSS Stationarity Test Results   \n",
      "=====================================\n",
      "Test Statistic                  1.088\n",
      "P-value                         0.002\n",
      "Lags                               20\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant\n",
      "Critical Values: 0.74 (1%), 0.46 (5%), 0.35 (10%)\n",
      "Null Hypothesis: The process is weakly stationary.\n",
      "Alternative Hypothesis: The process contains a unit root.\n"
     ]
    }
   ],
   "source": [
    "from arch.unitroot import KPSS\n",
    "\n",
    "kpss = KPSS(default)\n",
    "print(kpss.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Changing the trend does not alter the conclusion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    KPSS Stationarity Test Results   \n",
      "=====================================\n",
      "Test Statistic                  0.393\n",
      "P-value                         0.000\n",
      "Lags                               20\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant and Linear Time Trend\n",
      "Critical Values: 0.22 (1%), 0.15 (5%), 0.12 (10%)\n",
      "Null Hypothesis: The process is weakly stationary.\n",
      "Alternative Hypothesis: The process contains a unit root.\n"
     ]
    }
   ],
   "source": [
    "kpss.trend = 'ct'\n",
    "print(kpss.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Zivot-Andrews Test\n",
    "\n",
    "The Zivot-Andrews test allows the possibility of a single structural break in the series. Here we test the default using the test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        Zivot-Andrews Results        \n",
      "=====================================\n",
      "Test Statistic                 -4.900\n",
      "P-value                         0.040\n",
      "Lags                               21\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant\n",
      "Critical Values: -5.28 (1%), -4.81 (5%), -4.57 (10%)\n",
      "Null Hypothesis: The process contains a unit root with a single structural break.\n",
      "Alternative Hypothesis: The process is trend and break stationary.\n"
     ]
    }
   ],
   "source": [
    "from arch.unitroot import ZivotAndrews\n",
    "\n",
    "za = ZivotAndrews(default)\n",
    "print(za.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variance Ratio Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variance ratio tests are not usually used as unit root tests, and are instead used for testing whether a financial return series is a pure random walk versus having some predictability.  This example uses the excess return on the market from Ken French's data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            Mkt-RF          SMB          HML           RF\n",
      "count  1109.000000  1109.000000  1109.000000  1109.000000\n",
      "mean      0.659946     0.206555     0.368864     0.274220\n",
      "std       5.327524     3.191132     3.482352     0.253377\n",
      "min     -29.130000   -16.870000   -13.280000    -0.060000\n",
      "25%      -1.970000    -1.560000    -1.320000     0.030000\n",
      "50%       1.020000     0.070000     0.140000     0.230000\n",
      "75%       3.610000     1.730000     1.740000     0.430000\n",
      "max      38.850000    36.700000    35.460000     1.350000\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import arch.data.frenchdata\n",
    "ff = arch.data.frenchdata.load()\n",
    "excess_market = ff.iloc[:, 0]  # Excess Market\n",
    "print(ff.describe())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variance ratio compares the variance of a 1-period return to that of a multi-period return. The comparison length has to be set when initializing the test.  \n",
    "\n",
    "This example compares 1-month to 12-month returns, and the null that the series is a pure random walk is rejected. Negative values indicate some positive autocorrelation in the returns (momentum)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Variance-Ratio Test Results     \n",
      "=====================================\n",
      "Test Statistic                 -5.029\n",
      "P-value                         0.000\n",
      "Lags                               12\n",
      "-------------------------------------\n",
      "\n",
      "Computed with overlapping blocks (de-biased)\n"
     ]
    }
   ],
   "source": [
    "from arch.unitroot import VarianceRatio\n",
    "vr = VarianceRatio(excess_market, 12)\n",
    "print(vr.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default the VR test uses all overlapping blocks to estimate the variance of the long period's return.  This can be changed by setting  `overlap=False`.  This lowers the power but does not change the conclusion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Variance-Ratio Test Results     \n",
      "=====================================\n",
      "Test Statistic                 -6.206\n",
      "P-value                         0.000\n",
      "Lags                               12\n",
      "-------------------------------------\n",
      "\n",
      "Computed with non-overlapping blocks\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/mnt/c/git/arch/arch/unitroot/unitroot.py:1657: FutureWarning: Mutating unit root tests is deprecated and will raise an error in the first release of arch 5.x after August 2020. Create new test objects to change test parametrization.\n",
      "\n",
      "  warnings.warn(MUTATING_WARNING, FutureWarning)\n",
      "/mnt/c/git/arch/arch/unitroot/unitroot.py:1706: InvalidLengthWarning: \n",
      "The length of y is not an exact multiple of 12, and so the final\n",
      "4 observations have been dropped.\n",
      "\n",
      "  InvalidLengthWarning,\n"
     ]
    }
   ],
   "source": [
    "warnings.simplefilter('always')  # Restore warnings\n",
    "\n",
    "vr.overlap = False\n",
    "print(vr.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: The warning is intentional. It appears here since when it is not possible to use all data since the data length is not an integer multiple of the long period when using non-overlapping blocks.  There is little reason to use `overlap=False`."
   ]
  }
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